Eighty thousand people gathered in Athens' central Syntagma Square tonight to demonstrate against the presence of U.S. bases on Greek soil.

By local standards, it was a remarkably restrained display of anti-American sentiment. The size of the crowd was considerably smaller than most observers of the Greek scene had expected, given that the demonstration was organized by a number of peace groups that represented not only the governing Socialist Party, but also the militant Moscow-line Communist Party of Greece and other, smaller leftist organizations.

The demonstration had been condemned by the leading conservative opposition group, the New Democracy Party.

By contrast, the last time Greece's left-wing parties put their muscle behind an anti-American rally--on the anniversary Nov. 17, 1982, of the 1973 uprising against the colonels' junta--the crowd that filed past the U.S. Embassy in Athens was estimated at between 300,000 and 400,000 people.

Anti-American sentiment has persisted here since the 1974 fall of the junta, which many Greeks feel enjoyed the tacit acceptance of Washington.

It has found frequent and passionate public expression since the Socialist government of Andreas Papandreou took power 1 1/2 years ago on a platform of closing down the four major U.S. bases in Greece and pulling out of the North Atlantic Treaty Organization.

However, today's demonstration was clearly one with a difference. For one thing it came after a nationwide military and police alert by the government this past weekend in response to information that a military coup was being planned. The crowd's sedateness may have reflected its organizers' unwillingness to stage too fiery a public display at such a time.

They displayed sensitivity to timing once before, in changing the original Feb. 25 date of the demonstration to avoid holding it immediately following the departure of Soviet Premier Nikolai Tikhonov.

It is widely believed here that Papandreou will soon sign an agreement with the United States extending U.S. operation of the bases. Negotiations to reach an agreement, currently in recess, have been taking place between the Papandreou government and Washington in the Greek capital since October.

Papandreou has said such an agreement will include a time plan for the bases' eventual removal, but analysts regard this as an exercise in semantics designed to appease his own Socialist Party's left wing as well as the Communist opposition, which controls key labor unions. They believe a formula could be found for such a time plan that would be acceptable to Washington.

The size and tone of the demonstration tonight may be an encouragement for Papandreou, who is eager to reconcile the radical left to the idea that the bases will continue to operate into the medium-term future.