Barbara Timm, the mother of the youngest American hostage, was emotionally drained yesterday -- numbed by three weeks of alternating high hopes and despair.

"I just refuse to allow myself to go up on that [emotional] roller coaster again," she said after hearing news that the Iranian militants may turn over their captives to the Revolutionary Council in Tehran. "It means nothing to me."

The weeks of zigzagging events in Iran have been a time of torment for many of the hostages' families.

Hopes were raised as the United Nations investigative commission prepared to go to Tehran. But hours before its Feb. 23 arrival, the initial optimism turned to uncertainty and fear as Ayatollah Ruhollah Khomeini indicated the hostages would likely be held at least until April.

Timm's son, Marine Sgt. Kevin J. Hermening, 20, is among the estimated 50 hostages held at the U.S. Embassy compound since Nov. 4, and her feelings yesterday were typical of those expressed by relatives of other hostages.

Timm had put her faith in the optimistic forecasts surrounding the U.N. commission's visit. "I was very high," she said in a telephone interview from her suburban Milwaukee home. "And the drop down was just very, very painful."

For Dorothea Morefield, recent weeks have been similarly trying. "They've been just pure hell. It's just been up and down, and nobody really knowing what's going on," she said yesterday from San Diego. "The whole thing's been a nightmare."

Her husband, U.S. Consul General Richard H. Morefield, 50, is a hostage.

Nonetheless, Morefield expressed guarded hope that yesterday's statement by the Iranian militants might be a step toward the hostages' release. "I guess I'm incurably optimistic," she said. Relatives of other hostages voiced feelings ranging from similarly cautious optimism to doubt, skepticism and occasional anger.

Zane Hall was among the skeptics. His son, Army warrant officer Joseph M. Hall, 31, is a hostage.

"We've been hearing stuff like that for the last two weeks, and one [official] will say one thing and the next one will contradict it," Hall said in a telephone interview from Little Falls, Minn. "It's just like the little boy hollering wolf."

Hall also bitterly criticized the Carter administration for allowing deposed shah Mohammad Reza Pahlavi to enter the United States last year and for failing to end the four-month-old hostage crisis. The embassy takeover in Tehran followed the deposed shah's admission to the United States for medical treatment.

"I'm not happy with the Carter administration. I think it's an idiotic, bumbling damn mess," Hall said.

Jose P. Gallegos was among the cautious optimists. His son, Marine Cpl. William A. Gallegos, 21, is a hostage.

"I'm not really [filled with] high hopes, but I'm hopeful," he said from Pueblo, Colo. "It sounds like they're trying to do something with it finally."

Many of the hostages' relatives voiced resignation, saying they wanted to avoid drawing conclusions from yesterday's statement by the Iranian militants. They were prepared, they said, to let events unfold as they would in coming days.

"I can only speak for myself, but I imagine most of the families of the hostages are beginning to get a little wary of getting too happy too soon," said Eugene Lauterbach of Dayton, Ohio. His son, administrative employe Steven Lauterbach, 28, is a hostage.

"So often these things have been reported, and didn't work out the way they were supposed to," Lauterbach added. "We have become very dubious."

"I don't believe any of it 'till I see it -- I'm at the point where I don't believe anything anymore," said Jackie Persinger of Seaford, Del., mother of another hostage, Marine Sgt. Gregory A. Persinger, 22. "I'm down in the dumps," she added. "It's just been too long."

"I personally count it as a rumor -- like the many we've had before," said Louisa Kennedy of the District of Columbia. Her husband, economic and commercial officer Moorhead C. Kennedy Jr., 49, is among the captives.

"You can't put stock in anything until it really happens," said Mary Needham of Bellevue, Neb. Her son, Air Force Cpt. Paul M. Needham, 29, is among those being held. "It's 'show-and-tell' time now."