American officials, praising Algeria for its role as intermediary in the U.S.-Iran hostage negotiation, believe the episode will have an important impact on improving relations with the socialist government in Algiers.

Though it is not clear to what extent the Algerians share this view, a better relationship flowing from the ties formed in recent months could be a significant plus for the West, officials believe, because Algeria has an important voice among so-called Third World countries and because it could add to loosening Algerian ties to Moscow.

"To the extent that they even understand us a little better, it can have an important spillover" in that Third World, one State Department official said.

"There is no question that this has been an important episode and it is widely recognized that we owe Algeria a great deal, a major debt of gratitude," another official said. The Algerians, he said, put top government officials and central bankers "entirely at our disposal. They were superb intermediaries, meticulous negotiators . . . accurate, objective, impartial, patient and painstaking in every knotty issue."

"It can't help but have an important impact," he added, "on the Algerian image in this country with the public, the Congress and the new administration."

Before 1979, when President Chadhi Bendjedid took over after the death of the more radical and hard-line President Houari Boumediene, relations between Washington and Algiers had been bad for many years. The militant socialist leadership in the north African country had provided haven for terrorists and airplane hijackers and encouraged various national liberation movements.

In recent years, however, the Bendjedid government, in the view of U.S. and European diplomats, has become more pragmatic and relaxed, broadening its contacts with the West while etaining its revolutionary credentials and thus its voice in the world of developing and nonaligned nations.

According to U.S. officials, the Algerians have "shown and enormous amount of good will" during the trying hostage negotiations. Expressions of thanks were repeatedly extent by Deputy Secretary of State Warren Christopher on behalf of outgoing President Carter and Secretary of State Edmund Muskie. The Algerians, on the other hand, were more reserved and subtle, not wanting to be politically embarrassed by any public American embrace, officials indicate.

Though Algeria has serious economic problems, the country is rich in oil and natural gas and, even during the years of bad political relations, trade ties with the United States florished. I n the first six months of this year, for example, the United States exported $315 million worth of goods to Algeria, mostly technology and industrial products, while the United States imported $4.1 billion, mostly oil and gas.

But several other positive and little-noted developments in other areas of relations unfolded in the months before Algeria was brought in, at the suggestion of Iran, in November to serve as the third-party intermediary. It is the prospect of the positive experience of the hostage negotiations building on these earlier developments that leads officials to believe important improvements are possible.

Late in September, a U.S. Navy frigate docked at Algiers, the first American warship to visit there in 17 years and an event that was looked upon as an important sign by both sides.

In November, the United States quickly provided about $4 million in aid and medical assistance in the wake of a devastating earthquake in Algeria.

Though the Algerians have been, and still are, overwhelmingly dependent on Moscow for military aid, the United States are able to establish a defense attache in Algiers in the past year and Washington has approved an Algerian request to have a similar military liaison officer here.

Officials also say they have the feeling that Algiera wants to diversify its heavy reliance on Moscow for arms, and there is widespread agreement among western officials that Algeria is also clearly unhappy with Moscow's invasion of Afghanistan in December 1979.

On the negative side, the longstanding dispute with Algeria continues over American support of Morocco in the lingering war in the western Sahara against Polisario guerrillas, backed by Algiers.

Even here, however, some U.S. officials see some possibilities for at least an improvement in mutual understanding.

The crucial immediate bilateral problem, however, lies in a multibillion-dollar liquefied natural gas (LNG) deal between the two countries in which negotiators have failed to break a nine-month impasse over price.

In April, Algeria halted shipments to the United States after the Carter administration refused to accept Algeria's demand for tripling its LNG price. The Algerians argue that various forms of energy are interchangeable and that the price of their LNG should be brought into line with foreign crude oil import prices. Though only about 1.5 percent of U.S. LNG demand was supplied by Algeria before the cutoff, that was enough to make the United States Algeria's biggest LNG customer.

While State Department officials clearly would like to see an equitable solution for foreign policy reasons, the matter is mostly in the hands of the Energy Department, and the stakes are huge and controversial. Officials say the United States could not give Algeria a higher price without doing the same for Mexico and Canada, which together supply almost five times as much LNG as Algiers.

Thus, what Algerians may likely view as the first test of American gratitude is linked to a situation involving business and economic pressures in this country completely divorced from the hostage situation.