THE MEDIA BUSINESS; Paramount Sues Viacom Over Fees

Paramount Pictures, a division of Gulf and Western Inc., yesterday filed an $88 million lawsuit against Showtime Networks; its owner, Viacom Inc., and Viacom's parent, National Amusements Inc. Paramount said that Showtime, the nation's second-largest pay-television service, was refusing to pay all the fees to which it had agreed for the right to run 75 Paramount films.

The dispute, which has been going on for nearly a year, has been worsened by the fact that Paramount, which had had an exclusive agreement with Showtime, has since negotiated an exclusive agreement with Home Box Office, the Time Inc. rival of Showtime that is the industry's leading service. The suit was filed yesterday in Los Angeles Superior Court.

The dispute centers on the last five films in the five-year contract, films that Paramount was to deliver this year. The films - ''She's Having a Baby,'' ''A New Life,'' ''Permanent Record,'' ''Plain Clothes'' and ''Blue Iguana'' - have not been box office hits. Paramount contends that Showtime has refused to accept and pay for the films as a way to reduce its minimum liability for the 75 films. People close to the negotiations put that figure at about $300 million.

People close to Showtime expect the company to argue that Paramount did not deliver the five films within the time specified in the contract, and that the lapse between theatrical release and pay-television runs has not been acceptable. Therefore, Showtime is not obliged to pay for the films.

The amount under dispute for the five films is about $38 million. But Paramount is also asking for accelerated payments on the other films in the package, which brings the total amount sought in the suit to $88 million. Normally, payments are spread over a number of years, making them less valuable.

In 1983, before Viacom was acquired by National Amusements, Showtime scored a coup in acquiring the exclusive pay-television rights to Paramount films. Paramount's Many Hits

For several years Paramount has been either the leading film studio or the second most successful. Its hits include ''Flashdance,'' ''Trading Places,'' ''Terms of Endearment'' ''Star Trek III,'' ''Amadeus,'' ''Beverly Hills Cop,'' ''Witness,'' ''Star Trek IV'' and ''Fatal Attraction.''

Home Box Office and its sister service, Cinemax, have almost three times as many subscribers as Showtime and its sister service, The Movie Channel. Exclusive rights to films from a leading studio were therefore particularly valuable as a marketing tool.

Paramount says the contract between the two companies was based on a complicated formula in which a per-subscriber fee for each film license was calculated using the film's performance at the box office.

In turn, Showtime guaranteed Paramount certain subscriber levels. At the end of the deal, Showtime was required to pay Paramount as if it had met those levels even if it had not. On the other hand, if Paramount did not deliver as many films as promised, Showtime's guaranteed payment was reduced.

The suit says that Showtime has not grown as fast as it projected and that Viacom decided not to accept the five films so it could avoid paying the shortfall in its overall guarantee.

News of the suit did not reach Wall Street until after the markets closed yesterday and so had no effect on Viacom's stock or on rumors that Gulf and Western and Viacom were in merger talks.