In October 1981, Andreas Papandreou led his Socialist Party to power promising to pull Greece out of both the European Community and NATO. Today, under anxious western eyes, Papandreou's Greece took its turn as president of the European Community for the next six months.

For the Eurocrats interviewed in Brussels, headquarters of the 10-nation community that has become known as "the economic arm of NATO," the test of success for the Greek presidency will be simple. As one said, "It will be a success if Mr. Papandreou proves he can be a European first and a Greek second."

Up to now, while not moving to pull Greece out of either the community or NATO, Papandreou has acted the role of free spirit within both organizations, playing to a nationalistic gallery at home and frequently blocking consensus on key international issues such as East-West relations, disarmament and the Middle East. There is anxiety in Brussels now over whether the Greek prime minister will carry this free-wheeling style over to the community chair.

The greatest concern is over what attitude Papandreou will take toward the community's attempts at political cooperation. Although the 1957 Treaty of Rome establishing the grouping made no mention of it, the European partners have been moving toward a common foreign policy since the early 1960s and a "solemn declaration" favoring a common policy, called the Genscher-Colombo Plan, was signed at the last community summit in Stuttgart two weeks ago.

Greece endorsed the Genscher-Colombo Plan, but reserved the right of each member state to conduct its own national policy. Now EC officials worry that Papandreou, by insisting on holding to past Greek positions, could continue to block unanimity in political cooperation.

There are optimists in Brussels, however, who point out that Papandreou speaks with two voices, reserving his militant, anti-community rhetoric for Greek domestic consumption. They note, for instance, that his radical statements on the EC's need for independence from Washington were made to Greek journalists en route back to Athens from Stuttgart.

If that isn't sufficiently reassuring, the European optimists have a fallback argument. The powers of the presiding country, they stress, are limited in some fundamental ways. It is not, for example, empowered to make policy decisions for the community. Its job is, rather, to organize, chair and often host the meetings that represent the community's normal decision-making process.

They concede, however, that each country brings its own style to the presidency and is able to highlight certain issues by giving them priority for discussion. Papandreou has said, for instance, that he will press for a community initiative on the Cyprus issue, which has soured Greece's relations with Turkey since it flared again in the mid-1970s.

Another sensitive issue that Papandreou has singled out is the Middle East. In May, Greece dissociated itself from a community communique endorsing the Israeli-Lebanese troop pullout agreement, and Greece remains the only community member that does not recognize Israel.

On a third issue named by Papandreou, Central America, the Greek position is consistent with the European Community's views. The Stuttgart summit issued a statement highly critical of the Reagan administration's Central American policy.

On the economic side, Papandreou has said he will push for "convergence"--that is, trying to narrow the economic gap between the community's richer and poorer members, particularly by channeling more funds to its Mediterranean regions.