Alexander the Greek, whose armies swept in triumph from the Danube to the Nile, will be the subject of a treasure-filled exhibit that will begin a U.S. tour - in November 1980 - at the National Gallery of Art.

Though Egypt, Mexico and China have lent the United Stated their antiquities, "The Search for Alexander" will be the first such exhibition sent to Washington by the government of Greece. Greek law used to ban the "export" of antiquities, but the regulations were amended in July 1977 and loans are now allowed.

The Greek government and Time Life Inc. will accompany the show with an illustrated book and a six-part TV series on "The Search for Alexander." "We expect the impact to be huge," said Time-Life's Helga Halaki. "We hope to equal the success of the King Tut show."

The exhibit will include between 50 and 100 objects. "The list is not yet firm," said J. Carter Brown, the Gallery's director, "but it's getting firmer all the time." The tomb of Philip II of Macedon, Alexander's father, was discovered just later year. The chest of solid gold in which his bones were buried, and his gold-and-silver diadem, will both be displayed. Brown, who was in Greece within weeks of the discovery, said Philip's tomb contained "a spellbinding group of objects."

Alexander (356-323 B.C.), who was tutored by Aristotle, was leading troops in battle when he was just 16.

He became king at 20 when his father was assassinated. He was an extraordinary warrior. Before his death, in Syria, at the age of 33, he had crossed the Balkans and marched south into Egypt; he founded Alexandria and reached the Hindu Kush; he conquered much of Persia, as well as Tyre, Babylon and Gaza. Alexander was clean shaven, and his shaving set a fashion that survived in the Greece-Roman world for 500 years.

"The Seach for Alexander" will remain on view in Washington until March 1981. The exhibit then will travel to Chicago, Houston and Los Angeles, before returning to the East Coast to either Boston or New York. Thereafter it will visit Tokyo, Cologne, and Paris before it is returned to Greece at the end of 1983.