UNITED STATES
               SECURITIES AND EXCHANGE COMMISSION
                     Washington, D.C. 20549
                                
                            FORM 8-K
                                
                         CURRENT REPORT
                                
Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934
                                
Date of Report (Date of earliest event reported): March 22, 1999
                                
                                
                                
                                
                                
                                
                        CLECO CORPORATION
     (Exact name of registrant as specified in its charter)







         Louisiana                       1-5663                72-0244480
(State or other jurisdiction      (Commission file number)    (IRS Employer
     of incorporation)                                     Identification No.)




       2030 Donahue Ferry Road,
         Pineville, Louisiana                                71360-5226
(Address of principal executive officers)                    (Zip Code)

                                
Registrant's telephone number, including area code:   (318) 484-7400



                                
Item 5.  Other Events


PINEVILLE, LA., March 22, 1999 -- Cleco Corporation (CNL:  NYSE, PSE) plans
to buy back a portion of its common stock for use in its Employees Stock
Ownership Plan (ESOP), announced David M. Eppler, president and chief
operating officer.

"This buyback program is a continuation of a process begun in 1991 when 
Cleco's ESOP was first implemented," Eppler said.

"In 1991, the Cleco board authorized the repurchase of up to $30 million of
Cleco common stock for eventual issuance to ESOP participants when they
retire or otherwise leave the company.  Since then, we have repurchased
approximately $7 million of Cleco common stock, leaving a balance of $23
million to repurchase for the ESOP."

Eppler said the company had not repurchased stock for the program since 1994.
He indicated the stock would be repurchased in the future on an as-needed
basis or when the price of the stock looked particularly attractive.

Cleco Corporation provides retail electric services to approximately 242,000
customers in about one-third of Louisiana's parishes (counties).  Through
subsidiaries, Cleco also markets unregulated energy and energy management
services, engages in energy asset development opportunities and provides
distribution construction and engineering services throughout the southeastern
United States.



Item 7.  Financial Statements and Exhibits


(c) Exhibits

     1.  News Release dated March 22, 1999 announcing Cleco's plans to buy
         back a portion of its common stock.  The common stock will be issued
         to employees as they leave the company's ESOP plan.



                           SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.


                                         Cleco Corporation
                                            (Registrant)


Date: March 25, 1999                     /s/ Thomas J. Howlin
                                             Thomas J. Howlin
                                             Senior Vice President, Finance
                                             and Chief Financial Officer
                                             (Principal Accounting Officer)