ROCKY MOUNT, N.C. (AP) _ Jack A. Laughery will step down as chief executive of Hardee's Food Systems, the fast food restaurant company announced Tuesday.

Laughery will continue as chairman of Hardee's and will continue his service on the board of Hardee's parent company, Imasco Ltd. of Montreal.

Bill Prather, who joined the Hardee's organization four years ag as president and chief operating officer, will assume the duties of chief executive officer on Jan. 1, the company said in a news release.

Bob Autry, president and chief operating officer since 1988 of Fast Food Merchandisers Inc., the distribution and manufacturing company that services Hardee's Restaurants, will assume the title of chief executive officer of that organization at the same time.

Laughery has been chief executive officer of Hardee's for the past 16 years. During Laughery's leadership of the chain, Hardee's Food Systems has grown from 750 restaurants to more than 3,300 in 42 states and nine foreign countries.

During the same period, operating profits have grown at a compound annual rate of 22 percent. Sales for the company will exceed $3.5 billion for calendar year 1989.

As chairman, Laughery will spend a major portion of his time working closely with the Hardee's franchise community. ''There are exciting days ahead for Hardee's,'' Laughery said. ''My commitment to the chain is undiminished and I look forward to a continued relationship with Hardee's and its franchisees.''

Headquartered in Rocky Mount, N.C., Hardee's Food Systems says it is the third largest hamburger fast-food chain in the world.