The name of Army Capt. Harry G. Cramer will be added to those of the 57,939 casualties already engraved on the Vietnam Veterans Memorial. And thereby lies a sad story--one that is troubling, no matter how one looks at the facts.

By his family's claim, Cramer was the first fatality of the Vietnam War. In the Defense Department's view, it isn't so: Cramer died in an accidental explosion while training Vietnamese troops in 1957, four years before the date officially marked as the start of the war.

But the Vietnam Veterans Memorial Fund, the organization that is responsible for judging eligibility, notified the Cramer family on July 5 that the officer's name will be added by late fall.

"As far as being the first casualty of the war, I don't know," said Jan Scruggs, president of the committee. "It's a nebulous situation. But the fact is Cramer died there . . . . It's that simple."

Cramer was 31, the first Green Beret commander in Vietnam, when he died. The effort to add his name to the memorial was spearheaded by a son, Harry G. Cramer III, a 29-year-old Army captain stationed in San Francisco, according to Knight-Ridder Newspapers writer Megan McCaslin, whose reporting is the basis for this item. Winning the campaign took constant badgering of those in Washington, the son said.

Maj. Bob Shields, a Pentagon spokesman, said there are problems in pinning down a precise date for the war's start and deciding who should be listed as casualties. The earliest casualties now listed on the memorial date from 1959. He said seven other families are awaiting verification that relatives' deaths before that year were in the line of duty.