When the Stuttgart Ballet opens a two-week engagement at the Kennedy Center Opera House Tuesday evening, it will mark not only the company's first appearance here since 1979 but also the resumption of a Kennedy Center tradition -- the presentation of major dance companies from abroad.

The Stuttgart troupe will be the first foreign ballet company in four seasons to appear in the Kennedy Center's ballet series. For a variety of complex reasons involving both money and politics, it became harder for foreign companies to travel and more difficult for American sponsors to import them during the first half of the present decade, as compared with the past.

The new Stuttgart visit presages a turnaround, one which will have notable sequels in the 1986-87 season largely as a result of the Reagan-Gorbachev cultural exchange agreement reached last fall.

But beyond this, the Stuttgart Ballet itself is a monument to internationalism.

It's a staple of 20th-century ballet lore that the Stuttgart Ballet, which had been languishing in relative obscurity since its early days of glory under the great 18th-century choreographer and theorist Jean-Georges Noverre, first achieved global stature in modern times under the leadership of John Cranko, who was the company's director from 1961 to his untimely death in 1973.

What's not as often recognized is how extensively the company has merited the tag "international" since Cranko's time, and never more than today.

Cranko himself was the first of the company's numerous "transplants." Born in South Africa, he moved to England to study at the Sadler's Wells Ballet School, and choreographed prolifically for the Sadler's Wells (later the Royal) Ballet before his appointment at Stuttgart.

Marcia Haydee, artistic director of the Stuttgart Ballet since 1976 and the ballerina who was Cranko's chief source of choreographic inspiration, is another example -- a dancer born in Brazil, who also studied at Sadler's Wells and was pursuing a European career when Cranko invited her to join him in Stuttgart in his first year of tenure.

The list is lengthy. There's California-born Richard Cragun, who went on to become Haydee's principal partner and one of the world's leading male virtuosos. Vladimir Klos, a member of the Stuttgart Ballet since 1968 and one of the company's outstanding principals, is a native of Prague. Alan Beale, the company's assistant director, is an Englishman who met Cranko as a member of the Royal Ballet in the '50s.

Some of the links are closer to home. Stuttgart dancer Stephen Greenston was born in Alexandria, started his ballet training in Baltimore and continued his studies with the National Ballet in Washington. Another, more recently recruited company dancer is Katherine Batcheller, formerly of the Washington Ballet. James Tuggle, chief musical conductor for the Stuttgart Ballet since 1984, hails from Portland, Ore.

Altogether, the Stuttgart Ballet personnel roster represents about 20 different countries.

The company's Opera House programs likewise reflect a strongly international character. Opening night brings the troupe's "signature" ballet, "Eugene Onegin," choreographed by Cranko in 1965 based on the tale by Russia's Pushkin, with music by Tchaikovsky (not, however, from the composer's opera of that title). Wednesday evening will see the Washington premiere of "A Streetcar Named Desire," inspired by the Tennessee Williams play, with choreography by John Neumeier, the Milwaukee-born director of the Hamburg Ballet, and music by two Soviet composers -- Serge Prokofiev and Alfred Schnittke.

On June 3, at the start of the second week of the visit, the company will introduce a mixed repertory bill no less international in flavor. First will come Michel Fokine's "Les Sylphides" with its familiar Chopin music, as staged by a legendary former dancer and pedagogue of the Bolshoi Ballet, 69-year-old Olga Lepeshinskaya.

This will be followed by the virtuosic male quartet, "Canto Vital," choreographed by Azari Plissetzki, brother of the celebrated Soviet ballerina Maya Plisetskaya, to music by Austria's Gustav Mahler (and first seen in Washington, incidentally, as danced by the National Ballet of Cuba at the Kennedy Center in 1978). Finally, there'll be "Gaite Parisienne," choreographed by Brussels' Maurice Bejart to the Offenbach score as arranged by Manuel Rosenthal.

This last ballet is, among other things, a tribute to the Paris-based, Armenian teacher known as Madame Rousanne (1894-1958), whose pupils included not only Bejart, but also Leslie Caron, Roland Petit, Zizi Jeanmaire, Violette Verdy, Yvette Chauvire and Jean Babilee.

It is said that the arts know no international boundaries. Surely it would be hard to devise a more convincing illustration than the Stuttgart Ballet, in its leadership, its dancers, its musicians and its repertory.