Fairfax City, which loves a parade, wants to march to the beat of a different drummer.

The city of 20,750, whose resurgent civic self-esteem led it to adopt a new slogan ("Catch Our Spirit, Feel Our Pride"), is now in the market for an official march and has decided to hold a competition.

Composers have been invited to submit their entries, to be entitled "The City of Fairfax," by April 15.

The winner will get $500. The contest rules are rigorous.

Entries must be:

* Less than four minutes.

* Traditional and "appropriate for use by street bands in parade modes." "Evocative" yet "original with the composer."

* Previously unpublished.

The 65-member City of Fairfax Band, which mostly gives concerts, but marches on the 4th of July, has not had its own municipal melody to play at official functions.

The city arts commission plans to choose six finalists to conduct their marches at a concert of the city band in late May.

The winning march then will be chosen and played by the band before the city's Independence Day fireworks display.

"We think we have a great story to tell in the City of Fairfax, and this march is a way of telling it," said Mayor George T. Snyder.

On top of the cash award, the winning composer will have the right to afix the words, "Winner in the City of Fairfax March Competition, 1985" to published versions of his work.

There's solace for the runners-up, too. City officials say finalists may use the words "Finalist in the City of Fairfax March Competition, 1985" on published copies of their works.

The contest started a week ago. So far, city officials report, no entries have been submitted.