As Philippe Chatrier, the president of the International Tennis Federation, sat in the stands watching his countryman Yannick Noah, the problems of tennis seemed very far away.

The game seemed no more complicated than a high backhand volley. But, in an interview, Chatrier said he believed that exhibitions are a danger to the sport and now pose its most serious problem. "The credibility is seriously endangered by special events," he said. "Something will have to give."

Chatrier said today there are 10 tournaments and 10 players currently under investigation, including Ivan Lendl, for allegedly giving and taking guarantees. Chatrier said the tournament in Milan that allegedly gave Lendl a guarantee has not received a sanction and is not on the schedule for 1984 because tournament officials have failed to produce "certain documents . . . as evidence they didn't pay Lendl."

Chatrier explored the rule that allows players to enter exhibitions that conflict with tour events eight times each year. He said tennis officials are working on a plan that would set aside certain times of the year for exhibitions so that they do not conflict with scheduled tour events.

"We are trying to operate some surgery on the 1985 circuit," he said, intimating that the subject was discussed at this week's meeting of the Men's International Professional Tennis Council. "One of the problems is that the players are used to such freedom. We should free up those eight weeks or shorten the circuit if necessary but we should make sure that players don't ridicule the circuit."

Players are now required to commit themselves to only 12 tour events each year. Chatrier said he thinks that rule is "ludicrous" and that players should be asked to play 20 weeks. But he said he did not see that happening soon.

Chatrier said he thought a confrontation between tennis officials and agents who promote exhibitions for the players they represent is inevitable in the next two years. "They are a major factor in the game," he said. "We've got to have a gentlemen's agreement, a code of conduct to establish some boundaries."

Chatrier suggested that exhibitions are the root of the guarantee problem. "Why do they ask for guarantees? Because there are so many promoters willing to guarantee money to play in exhibitions . . . the tournaments have to beat that."

But he predicted that "exhibitions will self-extinguish and fade away because you can't fool the public all the time. They will realize it is pure show business as opposed to the tournament game.

"The only alternative is to say, 'We can't beat guarantees, let's join them.' Honestly, that would be a disaster."

The top players argue that they should be able to accept guaranteed appearance money because of the revenues their presence generates for tournaments.

Chatrier pointed out that players are allowed to maximize their income through "patch" deals and clinics arranged for them at tournaments where they compete. But these offers can also be used as inducements to guarantee their participation and are sometimes merely disguised guarantee payments. "It is always going to be a sticky problem," he said.

Guillermo Vilas, who is appealing his suspension by the Pro Council for accepting a $60,000 guarantee from a tournament in Rotterdam, has argued that he has been singled out unfairly. "Obviously we have nothing against Vilas," Chatrier said. "We suspect they all take guarantees. It was the first time we got the evidence. So we hit hard to show we mean business."

Despite the problems that he concedes threaten the integrity of the sport, Chatrier refused "to acknowledge that the game is in chaos."

Smiling, he called it "a healthy mess." One indication of that healthy mess is that the Pro Council recently turned down a $25 million offer from Volvo to continue its sponsorship of the Grand Prix for another five years. But Chatrier indicated that talks with Volvo are not closed. "I have a feeling we'll be talking soon," he said.

Clearly he views the problems of tennis philosophically, as growing pains the sport will endure. "At this moment, we are in such a star system," he said. "Honestly, the top players in the world are sitting on cloud nine. It's unreal. We have to be patient. It is a growth, a fever."