BUDAPEST, JULY 10 (TUESDAY) -- Fifty-one of an estimated 6,000 Albanians who flocked to their capital's foreign embassies in search of asylum flew to Prague early this morning, a development that prompted diplomats to express hope that a solution to the weeklong refugee crisis may be near.

{The flight from Tirana, the Albanian capital, was greeted by Czechoslovak Foreign Minister Jiri Dienstbier, who said his country got the asylum-seekers out through "a little luck and a lot of patience," the Associated Press reported.}

Forty more were reported preparing to leave Tirana for Hungary today, and Monday night West German, French and Italian embassy officials in Tirana were helping 4,500 refugees jammed into their embassy compounds fill out passport applications.

"They have received their passports and we are ready to take them out," the spokesman for the Hungarian Foreign Ministry, Istvan Sandor, said.

Czechoslovak Deputy Foreign Minister Vojtech Wagner said in Prague that nearly all of the 51 who left today want to go to the United States or Australia. Other countries have reported that many of the refugees holed up in their embassies also want to go to the United States, but officials said that the preparation of exit papers has been slowed because some of them are illiterate.

{In Washington, State Department spokesman Richard Boucher said he had no information about requests to travel to the United States and no comment on what U.S. policy would be toward such requests, the Associated Press reported.}

Several thousand Albanians streamed into foreign embassies last week, attempting to escape the last hard-line Communist state in Europe. The initial exodus tonight appeared to be the first tangible progress in a crisis that has overwhelmed several Western European embassies in Tirana and prompted a reshuffling of the Albanian leadership.

In a further government shake-up, Communist Party leader Ramiz Alia Monday replaced four cabinet ministers responsible for the economy. Over the weekend, the hard-line police minister and the war minister were fired and several other politicians were replaced with younger men. The shake-up is part of a power struggle in the Communist Party leadership between old-line Stalinists and moderate reformers loyal to Alia.

Dienstbier said in Prague today that "difficult" negotiations preceded Albanian approval for the flight of the plane sent by Czechoslovakia that removed the 51 Albanians who had taken refuge in the Czechoslovak Embassy.

In the West German Embassy, where some 3,000 asylum-seekers are crowded in unsanitary and deteriorating conditions (with one toilet for every 375 people), some progress also was reported.

A West German Foreign Ministry spokesman said Albanian passport application forms had been distributed to refugees in the embassy compound. Passport forms also were distributed at the French and Italian embassies, where an additional 1,500 refugees are camped.

West German Foreign Ministry spokesman Hanns Schumacher said in Bonn that he was confident all of the passport applications would be completed by tonight. But he said he had "no idea" when refugees would begin to leave the embassy, adding that it would depend on how fast the Albanian government reacted. Other reports from Bonn said officials hoped evacuation could begin as soon as today.

Earlier, Albanian authorities had accused the West German and other West European governments of dragging their feet in order to embarrass the Albanian government, and hinted that Bonn was reluctant to take in such a large number of Albanian refugees. Albanian authorities have refused to grant landing permission to West German cargo planes loaded with food and medical goods.

Monday night, Schumacher dismissed Albania's accusation as "absurd." He was quoted as saying that West German Embassy officials in Tirana were interviewing refugees to determine whether all of those who scaled the compound's walls during the rush last week wanted to go to West Germany.

Last week, West German Foreign Minister Hans-Dietrich Genscher promised that any refugee who wanted to go to West Germany would be received. Schumacher said he hoped other Western countries would do the same.

A U.N. spokeswoman said today that Secretary General Javier Perez de Cuellar remained "confident" that the refugee situation would be resolved within the week, but she added that it was still too delicate to give details.

The atmosphere in Tirana was reported calm today and the flow of refugees into the embassy compounds appeared to have nearly stopped. Albanian security police were seen in the embassy district Monday, after having been removed last week after firing at citizens who tried to climb embassy walls. Police reportedly set up roadblocks on the major roads into the capital today.

Albanian state television showed young men lounging in the embassy compounds. Outside, weeping and sometimes hysterical women prowled the fences and said they were searching for missing children.

The refugee crisis has left the Albanian leadership with a dilemma similar to the one faced by East German leaders last fall, when thousands of East Germans, frustrated by their government's failure to make reforms, fled to West Germany via its embassy in Czechoslovakia.

Albanian officials soon may learn whether leniency toward the existing group of refugees will encourage others to come forward.

Over the weekend, the Albanian parliament passed laws formalizing earlier promises by the government making passports available to all citizens who want them.

Albania, one of the poorest countries in Eastern Europe, has the same economic and social problems that brought down Communist parties in the rest of the region. Its 25-year-old Chinese-built factories are antiquated and unprofitable. It has the highest birthrate in Europe, and a population with a median age of 26.

Once a country of small towns and villages, it has become increasingly urbanized in the past decade. About 300,000 of its 3 million people belong to the Communist Party, according to Albanian diplomats. Analysts say the growing numbers of young unemployed people are unlikely to be satisfied with party blandishments.