When conservative American and European intellectuals gathered in Washington last weekend to ponder "The Trans-Atlantic Crisis," the well-known Italian author and columnist Luigi Barzini told them about his recent visits with officials at the Pentagon and White House.

"Everybody there told me that the Italians are doing a wonderful job," Barzini said. "But you never see that in the papers."

Today, the newspapers and television networks are filled with gratitude and praise from President Reagan and other Americans for the fine work of the Italian anti-terrorist force that rescued U.S. Army Brig. Gen. James L. Dozier.

Nevertheless, Barzini's point of the week before remains both accurate and important, especially when there is growing criticism and animosity between Washington and some allies in Western Europe over whether the alliance has any collective backbone in the face of developments in Poland, Afghanistan, the Persian Gulf region and other trouble spots outside Western Europe.

Whatever the troubles in the alliance, Italy has been a bright spot, as far as Washington is concerned, that ought to balance, at least in part, some of the problems with other countries.

In the past three years, in particular, Italy has played an increasingly important and positive role, even a crucial one on some issues, within the alliance.

* On the controversial question of deploying 572 new nuclear-tipped U.S. Pershing II and cruise missiles in Europe, the Italians have not wavered from their initial agreement in late 1979 to allow 112 cruise missiles to be based on their soil.

The Italian commitment is crucial to the project since the West Germans, who are receiving the bulk of the remaining missiles, have said they will not go along unless at least one other non-nuclear Western European country joins them. Belgium and Holland have thus far not agreed to accept the new weapons.

* In the Middle East, as Italian diplomats note, the Italians were the first to inform the Reagan administration that they would take part in the proposed peace-keeping force in the Sinai desert between Israel and Egypt.

The Rome government also played a key role in encouraging other West European nations to participate.

* The Italians have also gone further than other allies in Western Europe, and moved closer to the U.S. position, in showing their dissatisfaction with Moscow over the imposition of martial law in Poland.

The Rome government has announced that it will suspend negotiations on the huge gas pipeline deal between the Soviet Union and Western Europe pending improvement of the situation in Poland.

Although the Italians are not among the most prominent future participants in that project, their involvement is not insignificant.

Italian firms are would-be suppliers of compressors and pipe sections for that huge enterprise, and Italy could also wind up getting some 37 percent of its natural gas from Moscow if the line is built.

The Italian Communist Party, representing about 30 percent of the electorate, has been among the most vociferous voices condemning the Polish crackdown, with those denunciations issued earlier and in sharper terms than those of most western governments.

Italy, though a country of roughly the same size and population as France, England or West Germany, traditionally has not been thought of as a major European power. But the Italians have never accepted the idea that they should be overlooked, and they brought things to a head within the alliance early in 1979.

In January of that year the leaders of the United States, England, France and West Germany met on the island of Guadeloupe in the Caribbean in a "big four" summit.

The Italians, afterward, let it be known that there should be "no more Guadeloupes," warning the other nations not to exclude them from such major strategy sessions if they were expected to share in alliance responsibilities.

At the Washington conference sponsored by The Committee for the Free World, Barzini sought to counter the spreading view that the Atlantic alliance is facing a crisis.

There were so many deep ties between the United States and Europe, he said, that "it is almost impossible to conceive" of a fundamental split.

Rather, he said, several different factors were at work. "The Americans are roaring threats at the Russians" while at the same time West German Chancellor Helmut Schmidt "goes to the back door of the Kremlin" and explains to the Soviets that "The Americans are very angry and we are trying to calm them down."

This is not bad, Barzini believes, because "we need the Americans to shout at the Russians and the Americans need Schmidt" so that these split roles can work both sides of the problem.

But the West, he says, too often "probably overestimates the Russian threat" while not giving enough credit to a first-rate West German army and even to an Italian army which, he says, has never been better, another point that he feels is overlooked. should be "no more Guadeloupes," warning the other nations not to exclude them from such major strategy sessions if they were expected to share in alliance responsibilities.

At the Washington conference sponsored by The Committee for the Free World, Barzini sought to counter the spreading view that the Atlantic alliance is facing a crisis.

There were so many deep ties between the United States and Europe, he said, that "it is almost impossible to conceive" of a fundamental split.

Rather, he said, several different factors were at work. "The Americans are roaring threats at the Russians" while at the same time West German Chancellor Helmut Schmidt "goes to the back door of the Kremlin" and explains to the Soviets that "The Americans are very angry and we are trying to calm them down."

This is not bad, Barzini believes, because "we need the Americans to shout at the Russians and the Americans need Schmidt" so that these split roles can work both sides of the problem.

But the West, he says, too often "probably overestimates the Russian threat" while not giving enough credit to a first-rate West German army and even to an Italian army which, he says, has never been better, another point that he feels is overlooked.