"I am about to be executed," says Eli Wallach, leaning back on a comfortable sofa in his suite at the Watergate. "I don't know why, but I have been tried and convicted of something, and my friends have gone to the governor and my lawyers have exhausted all appeals and they come to get me and take me out of my cell."

The 63-year-old actor is recalling a recurring nightmare. It began years ago, long before he first took the role of Alexander Ivanov in Tom Stoppard's "Every Good Boy Deserves Favour." But the flavor of the role - a dissident in a Soviet mental institution - reminds him of the dream.

"Just as they are about to execute me, I wake up," Wallach says, smiling uneasily.

Victim-of-society roles have been running strong lately in the Wallach family. He has just finished a three-month off-Broadway run in "The Diary of Anne Frank" with his wife Anne Jackson and their daughters, Roberta and Catherine.

"And not too long ago," he recalls, "Anne was in a play called "Inquest," about the Rosenbergs. She didn't exactly enjoy the role - she went to the electric chair every night - but it was a role with some substance.

"If you want to do quality things, you're not going to make a fortune - for that you do a television series. But night after night, doing a show that comes to terms with human problems is very rewarding. You can feel yourself growing."

He feels that Ivanov is such a role - one that "asks the right questions even if it doesn't have all the answers."

Wallach ought to know - he's played Ivanov three times in two years.

When he opened in "EGBDG" at the Kennedy Center last year, Wallach recalls, "President Carter came backstage to say hello to the cast, and I didn't know what to say to him - I don't talk much to presidents. Finally, I told him, "I never dreamed the day would come when I would be older than the president of the United States," and he told me, "I always liked you." "

Wallach has been a stage actor since 1940, in plays ranging from Tennessee Williams ("Camino Real" and "The Rose Tattoo") to Shaw ("Major Barbara") and Ionesco ("Rhinoceros"). He made his film debut in "Baby Doll" (1956), and has appeared in dozens of films since then, including "The Magnificent Seven," "How the West Was Won," "The Good, the Bad and the Ugly" and "The Deep."

One of his specialties is using the Stanislavsky method on villainous roles - but it still bothers him that his role in "The Deep," a good guy in the book, was turned into a villain in the film.

He met his wife (the author of a book, "Early Stages") when they were playing together in an off-Broadway production of "This Property is Condemned," and they have acted together in movies such as "The Tiger Makes Out" and "How to Save a Marriage" as well as many plays.

Wallach doesn't know how to classify "EGBDF": "Is it a play with music, or is it a piece of music with scenery and dialogue?" But, he adds, "Whatever you call it, and short as it is, it's a rich pate. After it's over, you walk out disturbed and thoughtful."

His current appearance in the Kennedy Center Concert Hall through Aug. 19 follows a run at the Metropolitan Opera in New York. There is a possibility that it may be staged in Chicago and/or Los Angeles, and he would like to do it again - though he also hopes to squeeze in a movie role by the end of the year.

"It was quite amusing for me to be on the stage of the Met," he reflects. "I'm tone-deaf - can't carry a tune at all. But I love the acoustics there and in the Kennedy Center."

Wallach sips ice-cold grapefruit juice and chats easily about Washington (an acquaintance that dates back to 1956, when he played in "Teahouse of the August Moon" at the National), and other topics including his hobbies. Photography is one, and the conversation shifts to lenses, apertures and f-stops.

"I remember when I was working in "The Misfits' with Clark Gable and Marilyn Monroe," he muses. "Magnum had the contract for photos and every week they would send in a star photographer - people like Cartier-Bresson. I didn't bring out my camera at all, I was too abashed. Then on the last day I got it out and shot a whole roll. I'm glad I did - Gable was dead 10 days later."

He is also fond of tennis, collecting clocks, prints and engravings, visiting museums and doing crossword puzzles, in which he takes a peculiar personal interest:

"I do The New York Times puzzle every day, and fairly often I find my name in it - you know, "Actor Wallach." I enjoy that. Now, I get upset when the word they want is "Eli" and the clue is "- Whitney" or "- Yale.""

One of his favorite Washington pastimes is watching congressional hearings, and he says he is sorry the SALT hearings are not now in session. He recalls being here in "Waltz of the Toreadors" with Anne Jackson in 1973 and spending most of his free time watching the Watergate hearings. The last time they played together here was two years ago in "Absent Friends."

Although he has two homes - on Long Island and in western Massachusetts - Wallach clearly enjoys the footloose life of a traveling actor - particularly when he and Jackson can find roles in the same production, as they frequently do. He is amused now to be doing commercials for a New York bank after having been a Mexican bank robber in half a dozen films. But even his work in spaghetti Westerns has paid off in travel:

"They say, "Join the Navy and see the world,"" says Wallach, "but my experience is that you join the movies to see the world. Movie roles have taken me to Greece, Spain, Mexico, Italy, France, England, North Africa, Yugoslavia and Cambodia. I remember spending 3 1/2 months at Angkor Wat, making "Lord Jim." I got 10 days off and went traveling all over Southeast Asia, always staying ahead of the telegrams that said, "Come back.""

His face clouds as he thinks of what has happened in Southeast Asia since then, and he half changes the subject: "I wish we'd do more political plays."

During the conversation, Wallach's phone rings. It is Tom Stoppard calling from London to ask about the opening night of "EGBDF."

After a few minutes of transatlantic chitchat, Wallach is back on the subject of Stoppard, whom he considers a brilliant director and playwright.

"I remember last year, when he was directing us in "EGBDF," he would say, "Eli," and then have a long pause. During that pause, your whole acting career would run before your eyes."

The show has also brought him other memorable moments. During the run at the Metropolitan, Wallach recalls, "One night, the exiled Soviet dissident Alexander Ginzburg came backstage.

"I told him, "I saw you on television and cut my hair just like yours."

"Ginzburg smiled and said, "Mine has grown back."" CAPTION: Picture, Eli Wallach, by Ken Feil - The Washington Post