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                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  SCHEDULE 13G

                    UNDER THE SECURITIES EXCHANGE ACT OF 1934

                                 (AMENDMENT NO.)

                         Martin Midstream Partners, L.P.
                                (Name of Issuer)

                                  COMMON UNITS
                         (Title of Class of Securities)

                                    573331105
                                 (CUSIP Number)

Check the following box if a fee is being paid with this statement [ ]. (A fee
is not required only if the filing person: (1) has a previous statement on file
reporting beneficial ownership of more than five percent of the class of
securities described in Item 1; and (2) has filed no amendment subsequent
thereto reporting beneficial ownership of five percent or less of such class.)
(See Rule 13d-7.)

*    The remainder of this cover page shall be filled out for a reporting
     person's initial filing on this form with respect to the subject class of
     securities, and for any subsequent amendment containing information which
     would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).


SEC 1745 (2-95)                   PAGE 1 OF 8

CUSIP NO. 573331105                   13G                      PAGE 2 OF 8 PAGES


--------------------------------------------------------------------------------
1    NAME OF REPORTING PERSON
     S.S. or I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

     (A)  KAYNE ANDERSON CAPITAL ADVISORS, L.P.   - 95-4486379
     (B)  RICHARD A. KAYNE                        - 124-34-0063

--------------------------------------------------------------------------------
2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                   (a) [ ]
                                                                         (b) [ ]

--------------------------------------------------------------------------------
3    SEC USE ONLY

--------------------------------------------------------------------------------
4    CITIZENSHIP OR PLACE OF ORGANIZATION

     IS A CALIFORNIA LIMITED PARTNERSHIP

--------------------------------------------------------------------------------
                 5   SOLE VOTING POWER

                     0

                 ---------------------------------------------------------------
                 6   SHARED VOTING POWER

   NUMBER OF         (A) 249,264
    SHARES           (B) 249,264
 BENEFICIALLY
   OWNED BY      ---------------------------------------------------------------
EACH REPORTING   7   SOLE DISPOSITIVE POWER
  PERSON WITH
                     0

                 ---------------------------------------------------------------
                 8   SHARED DISPOSITIVE POWER

                     (A) 249,264
                     (B) 249,264

--------------------------------------------------------------------------------
9    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON*

     (A) 249,264
     (B) 249,264

--------------------------------------------------------------------------------
10   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*   [ ]

--------------------------------------------------------------------------------
11   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

     (A)5.90%
     (B)5.90%

--------------------------------------------------------------------------------
12   TYPE OF REPORTING PERSON*

     (A) IA
     (B) IN

--------------------------------------------------------------------------------

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                   PAGE 2 OF 8

                                  United States
                       Securities and Exchange Commission

                                  Schedule 13G

*********************

Item 1. (a) Issuer:         Martin Midstream Partners, L.P.
        (b) Address:        4200 Stone Road
                            Kilgore, TX  75662

Item 2. (a) Filing Persons: Kayne Anderson             Richard A. Kayne
                            Capital Advisors, L.P.

        (b) Addresses:      1800 Avenue of the Stars,  1800 Avenue of the Stars,
                            Second Floor               Second Floor
                            Los Angeles, CA 90067      Los Angeles, CA 90067

        (c) Citizenship:    Kayne Anderson Capital Advisors, L.P. is a
                            California limited partnership
                            Richard A. Kayne is a U.S. Citizen

        (d) Title of Class
            of Securities:  Common Units

        (e) Cusip Number:   573331105

Item 3. If this statement is filed pursuant to Rule 13d-1(b) or 13d-2(b), check
        whether the person filing is a:

        (e) Kayne Anderson Capital Advisors, L.P., is an investment adviser
            registered under section 203 of the Investment Advisers Act of
            1940.

Item 4. Ownership

        (a) Amount Beneficially Owned:

        Kayne Anderson Capital Advisors, L.P. Managed Accounts           249,264

        Richard A. Kayne                                                 249,264

        (b) Percent of Class:                                              5.90%

        (c) Number of shares as to which such person has:

            (i) sole power to vote or direct to vote                           0

            (ii) Shared power to vote or direct the vote                 249,264

            (iii) sole power to dispose or direct the disposition              0

            (iv) shared power to dispose or direct the disposition of    249,264


                                   PAGE 3 OF 8

                                  United States
                       Securities and Exchange Commission

                                  SCHEDULE 13G

                    Martin Midstream Partners, L.P. (Issuer)
                           **************************

Item 5.  Ownership of Five Percent or Less of a Class

         If this statement is being filed to report the fact that as of the
         date hereof the reporting persons have ceased to be the beneficial
         owner of more than five percent of the class of securities, check the
         following [ ].
         Not applicable.

Item 6.  Ownership of More than Five Percent on Behalf of Another Person.
         Not applicable.

Item 7.  Identification and Classification of the Subsidiary Which Acquired the
         Security Being Reported on By the Parent Holding Company
         Not applicable.

Item 8.  Identification and Classification of Members of the Group
         Not applicable.

Item 9.  Notice of Dissolution of Group
         Not applicable.

Item 10. Certification
         By signing below we certify that, to the best of our knowledge and
         belief, the securities referred to above were acquired in the ordinary
         course of business and were not acquired for the purpose of and do not
         have the effect of changing or influencing the control of the issuer of
         such securities and were not acquired in connection with or as a
         participant in any transaction having such purposes or effect.


                                   PAGE 4 OF 8

                                  United States
                       Securities and Exchange Commission

                                  SCHEDULE 13G

                    Martin Midstream Partners, L.P. (Issuer)
                           **************************

                                    SIGNATURE

     After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

                    February 9, 2005
                          Date


                  /S/ RICHARD A. KAYNE
-------------------------------------------------------
                  Richard A. Kayne


KAYNE ANDERSON CAPITAL ADVISORS, L.P.

By: Kayne Anderson Investment Management, Inc.


    By: /S/ DAVID J. SHLADOVSKY
        -----------------------------------------------
        David J. Shladovsky, Secretary


                                   PAGE 5 OF 8

               JOINT FILING AGREEMENT PURSUANT TO RULE 13d-1(f)(1)

This agreement is made pursuant to Rule 13d-1(f)(1) under the Securities
Exchange Act of 1934 (the "Act") by and between the parties listed below, each
referred to herein as a "Joint Filer." The Joint Filers agree that a statement
of beneficial ownership as required by Section 13(d) of the Act and the Rules
thereunder may be filed on each of their behalf on Schedule 13D or Schedule 13G,
as appropriate, and that said joint filing may thereafter be amended by further
joint filings. The Joint Filers state that they each satisfy the requirements
for making a joint filing under Rule 13d-1.

                    February 9, 2005
                          Date


                  /S/ RICHARD A. KAYNE
-------------------------------------------------------
                  Richard A. Kayne


KAYNE ANDERSON CAPITAL ADVISORS, L.P.

By: Kayne Anderson Investment Management, Inc.


    By: /S/ DAVID J. SHLADOVSKY
        -----------------------------------------------
        David J. Shladovsky, Secretary


                                   PAGE 6 OF 8

                                  United States
                       Securities and Exchange Commission

                                  SCHEDULE 13G
                                  (cover page)
                    Martin Midstream Partners, L.P. (Issuer)
                           **************************

Box 9. The reported units are owned by investment accounts (investment limited
       partnerships, a registered investment company and institutional accounts)
       managed, with discretion to purchase or sell securities, by Kayne
       Anderson Capital Advisors, L.P., as a registered investment adviser.

       Kayne Anderson Capital Advisors, L.P. is the general partner (or general
       partner of the general partner) of the limited partnerships and
       investment adviser to the other accounts. Richard A. Kayne is the
       controlling shareholder of the corporate owner of Kayne Anderson
       Investment Management, Inc., the general partner of Kayne Anderson
       Capital Advisors, L.P. Mr. Kayne is also a limited partner of each of the
       limited partnerships and a shareholder of the registered investment
       company. Kayne Anderson Capital Advisors, L.P. disclaims beneficial
       ownership of the units reported, except those units attributable to it by
       virtue of its general partner interests in the limited partnerships. Mr.
       Kayne disclaims beneficial ownership of the units reported, except those
       units held by him or attributable to him by virtue of his limited
       partnership interests in the limited partnerships, his indirect interest
       in the interest of Kayne Anderson Capital Advisors, L.P. in the limited
       partnerships, and his ownership of common stock of the registered
       investment company.


                                   PAGE 7 OF 8

                                   UNDERTAKING

The undersigned agree jointly to file the attached Statement of Beneficial
Ownership on Schedule 13G with the U.S. Securities Exchange Commission and
Martin Midstream Partners, L.P.

Dated: February 9, 2005


                  /S/ RICHARD A. KAYNE
-------------------------------------------------------
                  Richard A. Kayne


KAYNE ANDERSON CAPITAL ADVISORS, L.P.

By: Kayne Anderson Investment Management, Inc.


    By: /S/ DAVID J. SHLADOVSKY
        -----------------------------------------------
        David J. Shladovsky, Secretary


                                   PAGE 8 OF 8