LIMITED LIABILITY COMPANY AGREEMENT of ATLAS PIPELINE HOLDINGS II, LLC

Exhibit 10.2

LIMITED LIABILITY COMPANY AGREEMENT

of

ATLAS PIPELINE HOLDINGS II, LLC

THIS LIMITED LIABILITY COMPANY AGREEMENT made as of May 26, 2009 by and among ATLAS PIPELINE HOLDINGS II, LLC, a Delaware limited liability company (the “Company”), ATLAS PIPELINE HOLDINGS, L.P., a Delaware limited partnership (the “Class A Member”) and ATLAS PIPELINE PARTNERS, L.P., a Delaware limited partnership (the “Class B Member”) (the Class A Member and Class B Member are sometimes herein collectively referred to as “Members” or individually as a “Member”).

1.1 Formation. On May 26, 2009, the Company was formed as a Delaware limited liability company by the filing of a Certificate of Formation with the Secretary of State of Delaware in accordance with the Delaware Limited Liability Company Act (the “Act”).

1.2 Name. The name of the Company is ATLAS PIPELINE HOLDINGS II, LLC.

1.3 Purpose. The limited purposes of the Company are to engage in any acts and activities and exercise any powers permitted to limited liability companies under the laws of the State of Delaware.

1.4 Registered Office. The address of its registered office in the State of Delaware is 110 S. Poplar Street, Suite 101, City of Wilmington, County of New Castle, State of Delaware 19801. The name of its registered agent at such address is Andrew M. Lubin.

2.1 Management. The management of the business and affairs of the Company shall be vested exclusively in the Class A Member who shall have the power to do any and all acts necessary or convenient to, or for the furtherance of, the business and affairs of the Company and who shall have the power and authority to bind the Company. Except as set forth in Schedule A to this Agreement, the Class B Member shall have no right or power to manage the business and affairs of the Company, or to bind the Company.

2.2 Meetings. No meetings of the Members need be held. However, meetings of the Members, or any class of Members, for any purpose permitted or required under this Agreement or the Act may be called by any Member, or, if a meeting of a class of Members, any Member who is within that class.

2.3 Action by Written Consent. Any action by the Members or any class of Members may be taken in the form of a written consent rather than at a Member’s meeting. The Company shall maintain a permanent record of all actions taken by written consent by the Members or any class of Members.

3.1. Powers of the Class A Member. The Class A Member shall have the power to do any and all acts necessary or convenient to or for the furtherance of the purposes described herein, including all powers, statutory or otherwise, possessed by a member of a limited liability company under the laws of the State of Delaware.

3.2. Indemnification. Each Member shall, and any employee or agent of the Company may, in the Class A Member’s absolute discretion, be indemnified by the Company to the fullest extent permitted by the Act and as may be otherwise permitted by applicable law.

4.1. Title in Company Name. All real and personal property shall be acquired in the name of the Company and title to any property so acquired shall vest in the Company itself rather than in any Member.

5.1. Compensation and Reimbursement. The Class A Member may be reimbursed for all expenses incurred in managing the Company.

6.1. Required Contributions. The Class A Member shall contribute to the capital of the Company the amount specified on Schedule A. The Class B Member shall contribute to the capital of the Company the amount specified on Schedule A.

6.2. Limitation of Liability of Member. Neither the Class A Member nor the Class B Member shall have any liability or obligation for any debts, liabilities or obligations of the Company, or of any agent or employee of the Company, beyond such Member’s capital contribution.

6.3. Loans. If a Member makes any loans to the Company, or advances money on its behalf, the amount of any such loan or advance shall not be deemed an increase in, or contribution to, the capital contribution of the Member. Interest shall accrue on any such loan at an annual rate agreed to by the Company and the Member (but not in excess of the maximum rate allowable under applicable usury laws).

6.4. Capital Accounts. The Capital Account of a Member shall be its capital contribution increased by any allocations of profits under Section 8.2(a) and decreased by any distributions to it under Section 8.1 and any losses allocated to it under Section 8.2(b).

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7.1. Limited Liability Company Interest. The relative rights and preferences of the Class A Member and Class B Member, and their respective interests in the Company, are set forth in Schedule A.

8.1. Distributions. Distributions to a Member (in cash or in kind) shall be as set forth in Schedule A.

8.2. Allocations of Profit and Loss. (a) Profits for each fiscal year of the Company shall be allocated 100% to the Class B Member unless, with respect to such year, the Class A Member would be entitled to any distribution, in which event profits for such fiscal year shall be allocated between the Class A Member and the Class B Member in the ratio of the distributions required to be made to each of them.

(b) Losses for each fiscal year of the Company shall be allocated as follows: (i) first, to each of the Members in proportion to the amount of profits allocated to the Member for all previous taxable years until the sum of such losses equals the sum of all previously allocated profits and (ii) second to the Members in proportion to their Capital Accounts.

9.1. Elections. The Class A Member and Class B Member shall jointly make any tax elections for the Company allowed under the Internal Revenue Code of 1986, as amended, or the tax laws of any state or other jurisdiction having taxing jurisdiction over the Company.

10.1. General Transfer Restriction. The Class A Member may not transfer its membership interest in the Company without the prior written consent of the Class B Member. The Class B Member may transfer its membership interest in the Company (or any portion thereof in accordance with Section 10.2) to any person. For purposes of this Agreement, a “transfer” includes, but is not limited to, any sale, assignment, gift, exchange, pledge, hypothecation, collateral assignment or creation of any security interest.

10.2. Admission of Additional Members. Additional Class B Members may be admitted to the Company at the direction of the Class B Member upon execution of a counterpart signature page to this Agreement by the additional Class B Member. Schedule A hereto shall be deemed to be automatically amended to reflect the additional

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Class B Member’s interest upon execution of the counterpart signature page by the Class B Member and the additional Class B Member, and the references in this Agreement to the Class B Member or its interest in the Company thereafter shall be deemed to be to all Class B Members and their respective interests in the Company.

10.3. Withdrawal of a Member. No Member shall be entitled voluntarily to withdraw, resign or dissociate from the Company or assign its membership interest (other than in accordance with Section 10.1 hereof) prior to the dissolution and winding-up of the Company, and any attempt by a Member to do so shall be ineffective.

11.1. Events Triggering Dissolution. The Company shall dissolve and commence winding up and liquidation upon the first to occur of any of the following (“Liquidating Events”):

The Company shall not be dissolved for any other reason, including without limitation, a Member becoming bankrupt or executing an assignment for the benefit of creditors and any such bankruptcy or assignment shall not effect a transfer of any portion of a Member’s membership interest in the Company.

11.2. Liquidation. Upon dissolution of the Company in accordance with Section 11.1, the Company shall be wound up and liquidated by the Class B Member or by a liquidating manager selected by the Class B Member. The proceeds of such liquidation shall be applied and distributed in the following order of priority:

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11.3. Certificate of Cancellation. Upon the dissolution of the Company and the completion of the liquidation and winding up of the Company’s affairs and business, the Member shall, on behalf of the Company, prepare and file a certificate of cancellation with the Secretary of State of Delaware, as required by the Act. When such certificate is filed, the Company’s existence shall cease.

12.1. Fiscal Year. The fiscal year of the Company shall be the calendar year.

12.2. Method of Accounting. The Class A Member shall select a method of accounting for the Company as deemed necessary or advisable and shall keep, or cause to be kept, full and accurate records of all transactions of the Company in accordance with sound accounting principles consistently applied.

12.3. Financial Books and Records. All books of account shall, at all times, be maintained in the principal office of the Company or at such other location as specified by the Class A Member

13.1. Binding Effect. Except as otherwise provided in this Agreement to the contrary, this Agreement shall be binding upon and inure to the benefit of the Members and, subject to Section 10, their heirs, personal representatives, and assigns.

13.2. Governing Law. This Agreement shall be governed by, and construed in accordance with, the laws of the State of Delaware without reference to conflict of laws principles.

13.3. Severability. The invalidity or unenforceability of any particular provision of this Agreement shall be construed in all respects as if such invalid or unenforceable provision were omitted.

13.4. Gender. As used in this Agreement, the masculine gender shall include the feminine and the neuter, and vice versa and the singular shall include the plural.

13.5. Amendment. This Agreement may be amended only by a written instrument executed by all of the Members.

13.6. Entire Agreement. This Agreement constitutes the entire agreement of the parties with respect to the subject matter hereof.

13.7. Binding Agreement. Notwithstanding any other provision of this Agreement, the Members agree that this Agreement constitutes a legal, valid and binding agreement of the Members in accordance with its terms.

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13.8. Counterparts. This Agreement may be executed in any number of counterparts, each of which shall be deemed an original of this Agreement and all of which together shall constitute one and the same instrument.

(SIGNATURES CONTAINED ON FOLLOWING PAGE)

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IN WITNESS WHEREOF, the parties hereto, with the intention of being legally bound hereby, have caused this Limited Liability Company Agreement to be signed and sealed the day and year first written.

SCHEDULE “A”

LIST OF MEMBERS; DESIGNATIONS OF RIGHTS

List of Members

Designation of Rights

The powers, preferences and relative, participating, optional and other special rights of the Class B membership interest, and the qualifications, limitations and restrictions thereof are as follows:

1. Distributions. Commencing on the date the Class B Member makes its above-described capital contribution, the Class B Member shall be entitled to receive a distribution (the “Preferred Distribution”), payable quarterly, equal to 12% of the amount of Class B Capital (as such term is hereinafter defined). The Preferred Distribution shall initially be paid, at the Company’s option, in cash or by increasing the Class B Capital in the amount of the required Preferred Distribution (“Additional Capital Contribution”); provided, however, that until the Credit Agreement Termination (as such term is hereinafter defined), the Company may pay a cash distribution only to the extent the Class A Member has received distributions with respect to the 12% Cumulative Class B Preferred Units of Atlas Pipeline Partners, L.P. Upon the retirement of all indebtedness (the “Credit Agreement Termination”) under the Revolving Credit Agreement dated as of July 26, 2006 among the Class A Member, Wachovia Bank, National Association, as administrative agent and issuing bank and the other lenders signatory thereto (as amended, the “Credit Agreement”), all further Preferred Distributions by the Company to the Class B Member shall be paid in cash. The Company shall make no distributions with respect to the Class A Membership interest until all accrued and unpaid Preferred Distributions have been paid and the Class B Member shall have received distributions equal to the Liquidation Value (as such term is defined in paragraph 2, below) of its Class B membership interest. Thereafter, all distributions shall be made to the Class A Member. As used herein, “Class B Capital” shall mean the amount of the Initial Capital

Contribution made by the Class B Member, as the same may be increased by any Additional Capital Contribution or decreased by any redemption of the Class B interest pursuant to paragraph 3, below.

2. Liquidation Value. In the event of any liquidation, dissolution or winding up of the Company, either voluntary or involuntary, the Class B Member shall be entitled to receive, out of the assets of the Company available for distribution to Members, prior and in preference to any distribution of any assets of the Company to any other Member, the amount of Class B Capital plus all accrued but unpaid Preferred Distributions thereon (collectively, the “Liquidation Value”). The foregoing shall not affect any rights which the Class B Member may have to monetary damages

3. Company Redemption Rights.

(a) The Company shall have the option (the “Call Option”) at any time after the Credit Agreement Termination Date and from time to time thereafter to redeem some or all of the Class B interest for cash; provided, however, that the foregoing redemption must be exercised for no less than the lesser of: (x) $2,500,000, or (y) the remaining unpaid Liquidation Value.

(b) The exercise of the Call Option by the Company shall be subject to the transmission of a written notice of the exercise of the Call Option to the Class B Member (the “Call Option Notice”) no later than 10 business days prior to the date fixed in the Call Option Notice for redemption which shall specify the amount of the Liquidation Value of the Class B interest to be redeemed.

(c) On the applicable redemption date, the Company shall remit the applicable cash consideration to the Class B Member and the Liquidation Value of the Class B interest shall be deemed to be reduced by such amount as of such date. When the Liquidation Value of the Class B interest has been reduced to zero, the Class B interest (and all of its powers, preferences and relative, participating, optional and other special rights and the qualifications, limitations and restrictions thereof) shall be terminated and, thereafter, the only outstanding interest in the Company shall be the Class A interest.

4. No Senior Securities; Ranking. So long as the Class B membership interest has not been fully redeemed, the Company and its subsidiaries shall not, without the consent of the Class B Members issue any membership interest in, or other equity securities of the Company ranking senior to the Class B membership interest with respect to liquidation preference, distributions, the timing of redemption or voting rights.

5. Severability of Provisions. If any right, preference or limitation of the Class B Member set forth herein is invalid, unlawful or incapable of being enforced by reason of any rule or law or public policy, all other rights, preferences and limitations set forth herein, which can be given effect without the invalid, unlawful or unenforceable right, preference or limitation shall nevertheless remain in full force and effect, and no right, preference or limitation herein set forth be deemed dependent upon any such other right, preference or limitation unless so expressed herein.

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