INDIANAPOLIS, AUG. 18 -- When the regime from communist Cuba sends representatives to Middle America, strange occurences are to be expected. Politics have made their inevitable progress into the athletic arena here at the 10th Pan American Games, where fists are thrown and leaflets are flung.

Cuban boxers have charged into the stands to brawl with anti-Castro demonstrators; a U.S. weightlifter who defected from Cuba several years ago was labeled a "traitor" by his former countrymen, and an American pitcher has compared Fidel Castro to University of Michigan football coach Bo Schembechler.

The latest controversy centers around a Miami dance band with ties to Cuban exiles that has been chosen to play at the closing ceremonies. Cuban officials said Monday the selection of the band, Miami Sound Machine, is an affront to their country, and threatened again today to boycott the closing.

"If the band is there, we won't be. I want to see 20 dancing hula girls," said Cuban Olympic Committee president Manuel Gonzalez Guerra. Then he did the hula.

At least that was a rare jovial side to the nearly constant and sometimes physical debates that have taken place at the Games since they opened Aug. 9. Cuba's presence here represents the first time the country has sent a major athletic delegation to the United States since the Castro regime took over in 1959. And athletic officials and authorities of both countries have encountered many unfamiliar and difficult problems as a result.

A number of Cuba-related incidents have threatened the peace of the Games as words like "propaganda," issues like civil rights and accusations of betrayal are commonplace.

Among the incidents have been the Cuban Olympic Committee president being verbally accosted in his hotel elevator the first day of competition; pickets outside the baseball park before Cuba's first game and a subsequent fight afterwards; a verbal exchange outside the boxing ring between U.S. and Cuban fighters; nearly a dozen members of the Cuban boxing team charging into the stands Friday night to fight anti-Castro demonstrators; police escorting anti-Castro demonstrators from another baseball game, and finally, a fight between U.S. and Cuban handball players Sunday night after the U.S. tied the game with one second remaining and eventually won in overtime.

In addition, Cuba has protested the presence of both Soldier of Fortune magazine-backed leaflets offering $25,000 to any Cuban defector, and small index cards with local immigration service phone numbers that were quietly distributed by the Washington-based Cuban National Foundation.

But the core of the debate is the presence of the most visible protesters here, the Miami based anti-Castro group, Cuba Independiente y Democratica (CID).

Cuba has called the group's flags and banners "provocations," and has threatened not to tolerate them. CID, meanwhile, has charged that it was physically attacked at the boxing matches Friday night and the members' civil rights are being jeopardized.

Local authorities, who have tried to mollify both sides, have beefed up security. But tensions remain high and local organizing president Mark Miles said today that although CID and the Cuban delegation appear to be more cooperative after meetings with local law enforcement officials, whether more incidents can be avoided until the Games conclude Sunday remains a question.

What authorities fear most is a repeat of the boxing incident. A brawl broke out Friday night, when Cuban boxers rushed into the stands and fought with three CID members, sending two to the hospital.

According to Indianapolis police, a Cuban athlete claimed he was slapped as he tried to find his seat. CID says its members were peacefully displaying a banner when Cuban boxers tried to wrestle it away from them.

In the aftermath, Cuban officials, including chief of security Armando Guirola, asserted that the delegation would take matters into its own hands and respond to any more provocations.

Local authorities are in the awkward position of arbitrating between the two sides and permitting free speech.

"It's new to us, that's for sure, and we've jumped in with both feet," said Indianapolis police spokeswoman Barbara Sinclair. "The reality is that we have to find a balance that is not offensive to one and overprotective of the other. Cuba has a right to compete without harassment and the protesters have a right to speak and write and convey what they want to say. The problem is to provide that without creating a security or police state."

Progress appears to have been made. As a result of the boxing melee, Miles and chief of police Paul Anee met with Cuban officials warning them that any more forays into the stands would be met by a response from Indianapolis police.

But the Cubans remain on edge. On Monday, official Coronado Martinez sent a letter to Miles requesting a meeting to discuss security and Cuban Olympic Committee president Guerra stated, "There is no security or guarantees for us here."

Today, there were more meetings and the organizing committee in Indianapolis has promised to work with Guirola in protecting the Cubans from harassment at athletic events, while the Cubans have promised to tell their delegation to defer to law enforcement officials in case of a problem.

Miles is also considering limiting the size and type of flags and signs that can be taken into events, although he is awaiting a legal opinion on the matter. The Indianapolis police are working with FBI security here to gather early information on plans for any more demonstrations.

The primary difficulty that remains is an immovable ideological one on both sides. Cuban officials consider the CID's presence a provocation no matter how legal, and CID members insist on being there, even buying tickets near the Cuban contingent when possible. At a Cuba-Nicaragua baseball game Sunday, officers kept the two Cuban groups separate and escorted the athletes to the parking lot. That was an improvement over a Cuba-Antigua baseball game last week, when the Soldier of Fortune leaflets were flung, and CID members and Cuban coaches wrestled over yet another flag.

CID officials contend that they are not trying to provoke or harass, rather to send "a message that our enemies are Castro and the communist regime, but not our Cuban brothers," said CID spokeswoman Dr. Juana Isa of Miami. She said CID has obtained counsel in Indianapolis to consider whether charges can be filed against the Cuban delegation and to protect its rights.

"The police in Indianapolis were trying to protect the Games first and not us," Isa said. "We feel they must, because we were attacked. But I think they have changed their manner and are protecting everybody."

If there has been tension among athletes, it is of the competitive sort, although there was a bad moment when American Kelcie Banks defeated Arnaldo Mesa of Cuba in a controversial and close decision Sunday night. It seemed the situation was about to escalate when one Cuban allegedly tried to pick a fight, according to U.S. boxer Andrew Maynard.

Maynard, who is originally from Cheverly, Md., will be the center of attention when he fights Cuba's Pablo Romero in a light heavyweight semifinal Wednesday night. That could be a tense one, as Romero was one of the boxers who rushed into the stands Friday.

But when Cuba won three bouts over Americans Monday night, there was no sign of hostility, other than one Cuban boxer making noises like an ambulance siren. Juan Lemus of Cuba maintains it's all part of a long rivalry in the ring with the U.S.

"We came here with the spirit of sportsmanship," he said. "We have no animosity, it's not political. We just like to compete. It's our pleasure. And we like to compete against Americans."

Perhaps baseball pitcher Jim Abbott put the whole issue in perspective when the Games opened last week. Abbott, who does not have a right hand, is something of a folk hero in Cuba, where he hurled the U.S. team to an upset of the No. 1 team in the world this spring. While there, he met Castro at a banquet, and compared him to the head football coach at Michigan, where he goes to school.

"He's a lot like Bo Schembechler," Abbott laughed. "Castro is a whole lot bigger, he's about 6-4. But they both have that same air of intimidation."

The case of Robert Urrutia was touchier. In 1980, Urrutia defected when he lowered himself by his bed sheets out of a hotel window in Mexico City. He competed here against his former teammates, who labeled him a "deserter" and a "traitor."

Probably the most unexpected source of controversy has been that of the band selected to play at the closing ceremonies. Cuban officials said they are concerned the band will "provoke" further trouble because lead singer Gloria Estefan is a Cuban native now living in Miami. Her father was allegedly a body guard for the wife of former Cuban president Fulgencio Batista, who was overthrown by Castro in 1959.

Miles said the organizing committee did not know of the band's background when it was chosen. He added that Cuban officials have not told him they will not attend the closing ceremonies.

"It's just a Latin beat band," Miles said. "From our point of view it's a broad appeal band, a dance band."

Mario Vazquez Rana of Mexico, president of the Pan American Sports Organization, realizes that Cuba takes issue with the band, but also said he thought the delegation would ultimately attend.

They have one very good reason to. Part of the ceremony includes the passing of the flag to Cuban officials, signifying that they will host the 1991 Pan American Games in Havana.