The last two years, the Italian Open tennis tournament has been able to claim no better than second billing at Rome's Foro Italico.

Since last spring, dozens of alleged terrorists have been standing trial in a gymnasium just up the street from center court. Accused of aiding the assassins of Aldo Moro, the former president of the Christian Democratic party, defendants testified as this year's tournament started Monday. Yet this coincidence prompted little comment here. Instead, the prime subject has been the tournament's decline.

Once a prestigious event on the men's pro tennis circuit, the Italian Open used to draw the best players in the world. Even those who had no real hope of winning returned every year to enjoy the boisterous informality of the crowd, the warm sun and superb red clay courts.

But in recent years the tournament has struggled to attract highly ranked players who would, in turn, attract sponsors, paying customers and television viewers. Only 150 fans turned out for the opening match Monday.

In 1982, tournament promoters spent months negotiating an endorsement contract between John McEnroe and Lipton Tea of Italy that they believed would ensure McEnroe's participation in Rome.

But McEnroe twisted an ankle and failed to show up. Jimmy Connors, Guillermo Vilas and Ivan Lendl also declined to play, saying they wanted to prepare for the French Open, the first leg of the Grand Slam.

Over the past winter, the promoters, anxious to beef up the entry list, announced prize money had been increased to $375,000 and the top eight seeds would receive first-round byes. But even the promise of more money for less work didn't appeal to the superstars.

Although still under contract to Lipton and eligible for a bonus if he plays here, McEnroe again declined, as have Lendl, Vilas and Connors. The only top 10 players here were Jose Higueras and Jose-Luis Clerc, and Clerc was disqualified from the tournament Friday after he walked off the court during a doubles match Thursday night in a dispute over a line call.

Among tennis authorities, the conventional wisdom--at least the excuse offered to the press--is that the Italian Open has suffered because it falls the week before the French. According to this theory, top players don't want to exhaust themselves in Rome, then fly to Paris for two more grueling weeks on slow red clay.

But a cursory review of the record suggests the best way to prepare for the rigors of the French Open, which begins Monday, is to compete here. In the last decade, four of 10 Italian Open champions went on to win the French.

Insiders admit the troubles of the Italian Open are a microcosm of problems that afflict the entire circuit, all of which can be summed up in a word: money.

At a time when top-ranked men's players can command as much as $75,000 a night for exhibitions and over $1 million annually for endorsement contracts, the importance of tournament tennis has declined. Many stars limit their schedules to 12 tournaments a year--just enough to keep images polished and endorsement prices high.

Although top players aren't eager to enter events in which they may lose in the early rounds and come away with just a few hundred dollars, promoters are increasingly reluctant to risk money on tournaments in which they cannot predict who will show up and who will make it to the semifinals and finals.

This has resulted in the proliferation of special events, hyped-up encounters between stars in which promoters can control the cast of characters. To compete with these programs of orchestrated entertainment, some tournaments have had to take measures that violate the rules.

First, they offer top players guarantees, or appearance money, often more than $100,000 a week. Then they allegedly give these stars preferential treatment to improve their chances of winning.

Officials often excuse themselves with the explanation that the rule against guarantees is difficult to police, and agents argue endorsement contracts linked to specific tournaments shouldn't be viewed as illegal inducements. Still, few top players are willing to participate in any event--except Wimbledon, the U.S. Open and the French Open--unless they are assured in advance of earning a substantial sum above and beyond prize money.

Arthur Ashe, the U.S. Davis Cup captain; Harold Solomon, president of the Association of Tennis Professionals, and Buster Mottram, Britain's outspoken No. 1 player, have written articles condemning this practice and pointing out potential dangers.

Although most people in tennis say appearance money has become so pervasive there may be no better solution than legalizing it, Ashe has said he would resign his position on the council rather than rescind the rule. Ashe stresses what others in the game will admit if given anonymity: guarantees not only diminish the incentive of top players, they reduce the prize money available to everybody else and deceive the public. Currency laws here would make that type of inducement prohibitive.

There long have been rumors on the tour that certain players are beyond the rules. Now, according to the Philadelphia Inquirer, the Men's International Professional Tennis Council, which governs the sport, is investigating charges of illegal payments to Vilas. Friday, the paper reported Lendl is also under investigation. Two weeks ago, after losing to McEnroe in the WCT final in Dallas, Lendl accused officials of protecting McEnroe.

Such is life on the men's professional tennis tour.