JERUSALEM -- Two pictures in the home of Yona and Miriam Baumel reflect the obsession and the anxiety that dominate their lives, as well as the hopes raised by the prospect of an end to the Middle East hostage ordeal.
One picture stands on top of the living room TV set. It is a small portrait framed in white showing a slim young man with a dark mustache and thick dark hair. He wears an army uniform, open at the neck.
The man is their son, Zachary.
Another, much hazier photo hangs near the kitchen. It is a photograph of a TV screen displaying a tank flying a Syrian flag and carrying several men on the turret. Some may be captured Israelis.
What encourages the Baumels is that the men are alive and that the photograph was taken from Syrian television the afternoon Zachary bailed out of his tank in Lebanon. There is the chance that he is one of those men.
In the nine years since Zachary disappeared after the tank battle against the Syrians in Lebanon, the Baumels have traveled a discouraging route known to almost every family of a hostage. They have written to heads of state, visited parliaments, met with their government's allies and met with its enemies, all in an effort to learn if their son is alive.
He is one of three Israelis still missing from a battle fought June 11, 1982, against Syrian forces in Lebanon. He also has become a key element in the ongoing search for a formula to bring about a large-scale exchange of Western hostages held in Lebanon and Arabs held by Israel.
Israeli officials insist that the formula should be simple:
In exchange for the release of seven missing Israelis, Israel would release all its prisoners from Lebanon, about 400 in all. The seven Israelis must be accounted for, the government says. Whether dead or alive, they must be returned. Otherwise, no deal.
If he is alive, Zachary is 30 years old. He moved from New York City to Israel with the rest of his family when he was 9. In 1982 he was a part-time religious student, and like almost all other Israelis over 18, he was a part-time soldier. He was planning to enter Hebrew University when Israel's invasion of Lebanon enrolled him in a tank unit.
His tank and one other, each carrying four men, were hit in battle near Sultan Yakoub, in Lebanon's Bekaa Valley. One of the eight Israelis was killed, and two quickly found their way back to Israeli lines.
Two others were taken prisoner and were released in two different exchanges by Syria and a Syrian-sponsored Palestinian group in 1984 and 1985. Still missing are Zachary and two of his colleagues, Zvi Feldman and Yehuda Katz.
Zachary is very much alive to his family, which has tried to maintain something of a normal lifestyle while pursuing every opportunity to secure his release.
"I think that deep down we believe that Zach is alive," Mr. Baumel said yesterday, between calls from friends offering the latest rumors. "The bottom line is that we think he's going to come back, and we want him to come back to a normal family."
"We keep our sense of proportion," said Mrs. Baumel. "We know the world goes on."
So a birthday party for a granddaughter takes precedence over a TV interview. When Zachary's friends send wedding invitations, the Baumels join in the celebrations. His friends still call, and the calls are welcomed.
Mr. Baumel, who is a real estate salesman, has tried to put his negotiating skills to work on his son's behalf. He has often had to settle for a dribble of information arriving second- and thirdhand.
With the approval of the Israeli government, he traveled twice to Tunis, Tunisia, to the headquarters of the Palestine Liberation Organization, to try to negotiate a prisoner swap.
Mr. Baumel, an Orthodox Jew, took "one of the PLO boys" to lunch at Tunis' one kosher restaurant.
He traveled to Jordan to meet a person claiming to have seen Zachary's army identification tags. The person said that he knew people who knew people who had the tags, and that he might have seen Zachary himself. Mr. Baumel was encouraged.
Even better was information that came early this year -- Mr. Baumel will not say from where -- that Zachary and Zvi Feldman were alive. Mr. Baumel said he was told they had been moved closer to Beirut and were in the hands of Palestinians.
Frustration occasionally shows, as when Mrs. Baumel talks about Israel's abduction of Sheik Abdel Karim Obeid, the Shiite Muslim cleric kidnapped from his home in Lebanon in July 1989. Israeli commandos seized the Hezbollah militia leader to give them leverage in bargaining for the release of missing Israelis.
The act drew criticism for the appearance that Israel was taking hostages, too.
"I felt badly when it was done, because we are religious people, and we believe that what we do influences other people," Mrs. Baumel said. Later, she decided that the abduction was forgivable -- if it led to the release of her son.
"It was done only after they tried to negotiate," she said. "It was done only out of frustration with the entire thing."