Sometimes they get mail meant for each other. If their paths cross at diplomatic receptions, their conversation is formal and superficial. They speak the same language and share the same cultural heritage, but there is an enormous and sometimes painful divide between them.

The partition of their once united and powerful country left the German people on two sides of the superpower line. And although the flags of the German Democratic Republic and the Federal Republic of Germany hang side by side in the lobby of the State Department, the countries' almost 40 years under opposing political systems have produced widely differing German communities here.

"They live in two worlds," said Robert Gerald Livingston, a research professor in German studies at Georgetown's School of Foreign Service. "To see them at cocktail parties is to see two people making great pains to stand on other sides of room from each other."

For West Germans, the political situation of the two states is constantly undermined by the undertows of common language, traditions and history. For them there are two German states and one German nation.

"The relationship between East and West Germans abroad is strange," said Eberhard Heyken, press counselor at the embassy of the Federal Republic of Germany, or West Germany. "It is not like with the French or British because we belong to different systems, different military systems and yet, we are both German, we speak the same language, have the same culture.

But representatives of the East German government see it differently.

"We believe there are two nations," said Bernd-Michael Poetschke of the Embassy of the German Democratic Republic, or East Germany. "Because with two different political systems you get two different nations, different attitudes in people, different aspirations. Just like Austria is a separate nation. They speak German there but nobody says Austria and Germany should be one country."

West Germany's huge, modernistic embassy on Reservoir Road NW is staffed by about 150 people who live throughout the metropolitan area with concentrations in Potomac, McLean and Bethesda.

Including the large West German military representation here and the businessmen, students, academics, journalists and employes of the World Bank and the International Monetary Fund, the West German community is about 1,500 strong. There is even a government-subsidized German School in Potomac, where 600 students are enrolled in grades from kindergarten through high school.

In contrast, the East German embassy employs only about 30 people and has been located on the two top floors of an office building at 1717 Massachusetts Ave. NW since the United States recognized the Communist state in 1974.

Home for all but a few top officials and the ambassador is an apartment building at of S. Arlington Ridge Rd. and S. Lynn Street in Arlington. The plain brick exterior is relieved only by a back-yard swimming pool and a child's painting of the sun on a window.

Neighbors say the East Germans keep to themselves; as one nearby resident said, "You'd never know they were there; they don't bother anybody." There is a school for early grades in the building and teachers regularly take the children for walks in the neighborhood.

"There seems to be a close-knit feeling between the families because there is a lot of laughter when they are playing," said one neighbor.

Apart from the embassy staff, the only other East Germans in Washington are four correspondents from East German state-run news media. In contrast, there are 47 journalists from West Germany in Washington.

Although East Germany has the highest standard of living in the East European bloc, foreign currency restrictions limit its activities overseas.

One West German television correspondent recalled that when Detroit's unemployment was a major story last year, he and his crew flew there to cover the story. Ten days later, he said, the East German television crew arrived. They had come by car.

"This is speculation but I would guess it's not too easy for the East German correspondents to live in an expensive environment like Washington," said Fritz Pleitgen, bureau chief of ARD, West German radio and television. "They don't have a lot of hard currency and they can't afford expensive restaurants."

Unlike Soviet diplomats who are under travel restrictions in the United States, the East Germans are free to go anywhere. However, one U.S. official said, "They stick together; they do things in groups and are discouraged from doing things off on their own. They go on trips to Harpers Ferry, they go to museums, but it's a controlled environment. They are very apprehensive. They have a sense of being isolated in hostile territory."

"In Moscow, in Poland, and Czechoslovakia, they are a bit more relaxed, they know the countries and have a feeling they are welcomed," said Arno Mayer, bureau chief for the West German wire service, Deutsche Presse-Agentur. "They don't have that feeling in Washington; it must be a very strange country for them."

Embassy spokesman Poetschke said security was a reason the embassy declined to have anyone interviewed for this article.

"Any questions are somewhat connected with security," said Poetschke, "there is a security problem in any country . . . but the risk is somewhat higher here because of the concentration of diplomats and the overall high level of criminality in this country with people going around shooting presidents. Obviously that doesn't happen in our country," he added.

"We like our life here living in a rather unrecognized way," said Poetschke, emphasizing that one reason to avoid publicity is so "some fool will not do something foolish."

But the anonymity that East Germans have sought here has also worked against them.

When their government sponsored an exhibition of art from Dresden for the opening of the East Wing of the National Gallery of Art in 1978, many visitors thought it was courtesy of the Federal Republic of Germany; their letters to the West German embassy said so.

"It demonstrates the East Germans' problem--how they're living in the shadow of their big brother, so to speak," said one U.S. official.

"People all weren't aware that Dresden was on the other side," said West German embassy's cultural counselor Haide Russell.

But West Germans are very conscious that "East Germany includes the heartland of Germany's culture--the places where Bach, Luther, Goethe were either born or lived," said a West German who works for an international agency here.

And the ancestors of many who regard themselves as German-Americans came from places in what is now East Germany. However, in this year's U.S.-West German celebrations during the tricentennial of German immigration to this country, the lines of heritage were blurred, though the actual division of the two Germanys was not. The East German government was not invited to join in the celebration, envisioned as a vehicle to stress the values that West Germans and Americans share. One critic termed it "half a celebration."

But the East German embassy spokesman Poetschke suggested a desire to remain distinct was another reason for not granting an interview for this article. "We are trying to avoid situations which put us together with the West Germans," said Poetschke. "We don't want to be mashed together in the same pot."

"The East Germans are also concerned about what the Soviets will imagine; the East bloc is tight and everybody knows everybody." They are concerned that "in the Soviet eyes the two Germanys will be seen operating together in any way," said Professor Livingston

Although the two states normalized their relations in 1972, contact between the two groups here is still tinged with what one West German journalist called beruehrungsangst, or "fear of touch."

"It was a famous expression during the '60s and '70s when both sides shied away from contacting each other," said Pleitgen, who added that West Germans feel differently toward East German officials than they do toward ordinary citizens."We have this strange relationship with the officials but not with the normal and average citizens; of course they are Germans; we know they are close to our ideas, the average person, they watch West German TV."

Many West Germans say one reason for their lack of contact with East Germans here is because the East Germans are officials who are always "on duty," and aren't free to express their personal beliefs.

West German journalist Mayer said, "Usually those people sent here by East Germany are reliable; they stick to official language and it's not really thrilling to have ideological discussions because once you did it, you know it and you're not eager to do it 100 times."

"I think it would be better if the East Germans had some independence to do what they like. They shouldn't be bad Communists but have some freedom; a little bit of independence, personal and political, to meet other people," said journalist Dietrich Moeller. "I'm sure a lot of West Germans would be glad to meet them--not to talk only about politics. It would be fine if we could meet them as we do with people from Switzerland or Austria."

Then he added, "Maybe in 20 years."