The first Soviet dancer to defect to the West was incorrectly named in yesterday's Style section. It was Rudolf Nureyev.

Thirty-six Nicaraguan men, women and children walked across the Mexican border into Texas without benefit of visas one day last month. Instead of hiding from U.S. immigration officials, they headed straight for the U.S. Border Patrol office in McAllen, Tex., turned themselves in and asked for political asylum.

Just two weeks earlier two Polish stowaways had emerged from crates on the docks of Baltimore. Haled before immigration authorities, they filed for political asylum.

Almost daily, Salvadorans living illegally in this country appear at deportation hearings; increasingly they ask for asylum. And 2,000 Haitians now being detained say they intend to do the same when their hearings are held.

More people are requesting political asylum in this country than at any other time in U.S. history. A record number of applications--more than 105,000--is now on file with the U.S. Immigration and Naturalization Service. Until just two years ago, when Congress significantly broadened the eligibility requirements, the average number per year was around 2,500, according to an INS spokesman.

Numbers are not the only change. Once primarily a passport to this country for the disaffected elite of Communist countries, political asylum, which enables a foreigner persecuted in his homeland to circumvent U.S. immigration laws and remain in this country indefinitely, now is being requested by average citizens from all walks of life and a wide range of countries.

The flood of requests has added a new element to the already controversial debate over the nation's immigration policy. Some federal officials charge that many requests are being filed solely with the ulterior motive of buying time for illegal immigrants who normally would be deported.

"Political asylum is being used as a ploy to obtain additional time to remain in the U.S.," said Kellogg Whittick, INS district director for Washington and Virginia. "Even if these claims are very weak, they have to be given consideration. And while the case is being assessed, they are given time in the U.S."

The upsurge has so clogged the bureaucratic machinery dealing with asylum applications that it has "completely broken down," in the words of one Justice Department official, causing long delays in getting responses to applications.

It also has brought closer scrutiny of the asylum process by civil rights, minority and congressional groups, some of whom charge that an objective review of asylum petitions and the human rights of an individual sometimes are overridden by the dictates of foreign policy.

Specifically, critics mention "a pattern of denials of asylum" for Haitians and Salvadorans because the U.S. government supports both those governments.

"It's embarrassing for the U.S. to call people from quote friendly governments unquote refugees," said Steven Horblett, legislative aide to D.C. Del. Walter E. Fauntroy.

Horblett also charges a racial motive for a long delay in adjudicating Ethiopian asylum petitions, some of which have been pending since 1977.

Still other critics question why members of the Soviet elite--ballet dancers for example--get asylum although they could not really be said to be persecuted at home. "A Soviet ballerina is not granted asylum because of political persecution, but to embarrass the Soviet Union," said Robert Remes, an immigration lawyer.

More than half the 105,000 requests for asylum that are on file are from Cubans who came in the l980 Mariel freedom flotilla. Iranians are next, with 14,778 applications, followed by 10,938 Nicaraguans, 10,287 Salvadorans, 5,646 Haitians, 3,843 Poles, 1,457 Ethiopians, 1,114 Afghans, 751 Chinese from Hong Kong and Taiwan, 745 Lebanese and 673 Iraqis.

According to the statistics, few Salvadoran or Haitian petitions for asylum have been successful. From July l980 through last March, only nine Haitians were granted asylum here, although more than 5,000 Haitian applications were on file during that period. And between October l980 and March of this year, only 26 Salvadorans have been given asylum.

Ethiopians have experienced long delays in getting their petitions reviewed, but in l980 and l981 they ranked third and in l982 they were fourth among nationalities receiving approvals for asylum.

Other nationalities whose applications were approved in large numbers in the past 2 1/2 years include Iranians, Afghans, Nicaraguans and Poles. Under legislation now before Congress, Cubans who applied for asylum will be given the opportunity to apply for permanent residence here.

Melvin Levitsky, the State Department official who oversees applications, for asylum, flatly denies allegations of political or racial bias. Ethiopian claims were not reviewed, he says, because under a special exemption Ethiopians were allowed to stay in this country anyway for several years after the Marxist revolution there.

Levitsky, senior assistant deputy secretary of state for human rights, said most Haitians have been coming to the United States because their own country was poor and that, while El Salvador has a "general climate of violence," this is not enough for asylum.

"The individual still has to prove he specificially would be persecuted; that's what we look at . . . , " he says. "Asylum is not designed for those fleeing civil or guerrilla war or because it's a poor country . . . . Random violence, as unfortunate as this may be, is not a condition on which asylum is granted . . . . Asylum is not a substitute for an immigration program."

As for Soviet claims, Levitsky says: "We give asylum based on the knowledge of what happens to people when they go back, and we know that a Soviet who wanted to defect and went back would be persecuted."

Population increases, lack of economic opportunities in poor countries, as well as revolutions, invasions and wars have all contributed to the surge in applications for asylum. But the main reason is a change in immigration law enacted by Congress two years ago to revise a policy that had its origins in the Cold War.

Under the old law, asylum covered only those fleeing the Communist bloc or the Palestinian-Israeli conflict in the Mideast. For anyone in these categories, asylum was virtually automatic; for anyone else, it was next to impossible.

In l980 Congress redressed this bias as part of a comprehensive overhaul of U.S. refugee legislation. It opened political asylum to all nationalities by incorporating into U.S. law the United Nations definition of a refugee (or asylee). Under that definition, anyone who can show a "well-founded fear of persecution on account of race, religion, nationality, membership in a particular social group or political opinion," is eligible for asylum or refugee status in the United States.

"For the first time in our history, the U.S. has become a country of first asylum on a mass scale," said Dale Schwartz, national secretary of the American Immmigration Lawyers' Association. "We used to be a place where, except for the isolated instances of a Soviet ballet dancer or a seaman jumping ship, refugees applied somewhere outside the U.S. and came here in an orderly fashion . . . but we never anticipated that nearby nations like Cuba, Haiti, would become unfriendly or that conditions there would become such that hundreds of thousands of people would flee or want to come to the U.S."

In theory, someone seeking political asylum differs from a person seeking refugee status only by the fact that he is already in U.S. territory. But in practice, this fact gives asylum-seekers a distinct advantage. A person asking for refugee status overseas has a one-shot chance: an interview with an INS official, whose decision cannot be appealed. In addition, there are yearly refugee quotas set by Congress.

A person seeking asylum, however, makes his request to a local INS district director who asks the State Department's Bureau for Human Rights and Humanitarian Affairs for an "advisory opinion." Although called advisory, INS almost invariably follows the the State Department's reply, INS officials admit.

But if the request for asylum is turned down, the applicant can appeal it through several layers of the INS and eventually challenge it in the federal courts, if he has the money and time to do so. And there is no limit on the number of persons who can be granted asylum in one year.

More importantly, an applicant cannot be deported while his petition is being considered. "You just don't move a person with an asylum application pending," said one INS deportation officer. This is becoming more widely known among those seeking to enter the U.S., as last month's unusual action by the Nicaraguans suggests.

For U.S. Chief Patrol Agent Larry Richardson, in McAllen, Tex., the idea that the Nicaraguans' actions might become a trend "is a terrifying thought. What it amounts to is that anyone can come across the border and automatically stay as long as he wants to fight you on removal. It's frustrating to our efforts to prevent illegal immigration."

Congress presently is considering proposals that would streamline the asylum procedure and meet criticisms about foreign policy interference. Applications for asylum would be considered by 70 independent "immigration judges," attached to the Justice Department and versed in immigration law and international relations.

Court review of denials of asylum would be sharply curbed and an alien would have only 14 days to file for asylum after notification to depart from the United States.

"These changes will give the system a chance to work, and will be doing good for those people who have genuine claims," says David Hiller, a senior Justice Department official. "It will separate them from those who are essentially gate-crashers and who are using asylum as a pretext to stay in the U.S. "

While the attempt to have decisions on asylum removed from the State Department is welcomed by many groups, lawyers are concerned over the attempt to reduce judicial review for asylum decisions.

"This really disturbs me," Schwartz said. "It scares me to leave final decisions to administrative officers; you tend to get a totalitarian mentality