THE LAST TWO weeks of tennis matches in the U.S. Open conveyed an extraordinary message: millions of American may not be interested in tennis, but millions will turn out for matches and watch on television to see obnoxious personalities perform.

At first, bad manners in tennis seemed to be the personal problem of a few young mavericks operating in a traditionalist's game of proper white clothes and decorum. But now the insulting gestures, the game delays and tantrum-like verbal attacks on game officials are becoming as regular as the bounce on Hartru. John McEnroe and Ilie Nastase are as well known for this misbehavior as for their tennis. And their behavior is being rewarded by the public with attention -- and cash. Large numbers of people apparently want to see this sort of thing. The newspapers carry detailed, curse-by-curse coverage that makes the final score almost an afterthought. TV news programs give ugly antics precious air time while mere good tennis does not otherwise merit any mention.

To tennis promoters the public's interest is a mandate. Good tennis players are fine but tennis players who can be offensive or obscene are money-makers. When a referee would brook no more abuse from Mr. Nastase during a recent match and ruled that Mr. Nastase was the loser by forfeit because of his behavior, tournament officials reversed the ruling and had the game continued without that referee. It seems clear who they thought was not acting in the best interest of the game.

However, tennis players and promoters may be hurting themselves in the long run by taking this new "let's be nasty" attitude. A few years ago the hockey establishment found it could attract more fans and public attention with bloody fights between the players. The brawls sparked talk about hockey among people who had never seen a game. Some of those people even paid the price of admission to a hockey game for the first time. Outrage about the fights was seen as moralistic and boorish. But the additional fans drawn by the blood could not replace the number of people lost when the game became a sloppy replica of good sport. Now hockey is changing, bringing the art back into the game.

It would be a smart move for the people behind the tennis game to take a lesson from hockey. Tennis officialdom should come down hard on the new antics. They may be bringing notoriety and cash to the game now. But promoters could soon find that they aren't able to draw a crowd without the players' going one step further in offensive behavior and coming right out and beating each other with their rackets.