A member of the State Department psychiatric team that examined the freed American hostages said yesterday that their mental health is "remarkably good," and that there is no basis for reports that about a dozen of them have serious psychiatric problems.

Dr. H. C. Haynes, a psychiatrist who met the 52 former captives in Wiesbaden, West Germany, and accompanied them home, said the psychiatrists and psychologists who examined the group last weekend concluded that "none of the people are psychotic . . . none need hospitalization."

Haynes said only three or four of the former hostages seem to have mental health problems that might need treatment.

"I was surprised at the statement that there are a dozen with severe problems," Haynes said. "None of the doctors could figure out where that came from."

At a press briefing Monday, White House press secretary James S. Brady said "about a dozen or so of the freed hostages were experiencing "severe problems . . . mostly mental." He said President Reagan had been so informed during a meeting with Defense Secretary Caspar W. Weinberger and Secretary of State Alexander M. Haig Jr.

At their news conference at West Point Tuesday, the former hostages said their group was in good psychological shape.

"I don't know how the rumors got out about some of us hostages supposed to be suffering from some mental condition," said Marine Sgt. John D. McKeel Jr. "I feel, from the people I've been talking to since my stay here in West Point, that we're all all right."

Haynes was the State Department's mental health director until August, and is now in private practice. He was on the team of about 15 psychiatrists and psychologists from the State and Defense departments who went to Germany last week to examine the freed captives. Each of the doctors examined two to four of the hostages and then discussed their findings among themselves.

"There had been a number of predictions [before the 52 were freed] of doom and gloom from a number of experts," Haynes said yesterday. "But they were wrong . . . . I would say, as a group, [their] condition is remarkably good."

In Germany Friday, State Department medical director Jerome Korcak said a number of the freed Americans exhibited "transient psychiatric ailments," including guilt and depression. Haynes said yesterday that Korcak meant that three or four of the hostages had these symptoms.

Haynes said the hostages emerged in better shape than some mental health experts had predicted because the predictions were based on experience among prisoners of War in World War Ii, Korea and Vietnam.

"A comparison to the POWs would be misleading for this group," Haynes said, because prisoners of war endured longer confinement and more brutal treatment.

Haynes said the psychiatric examinations showed the hostages to be a group of strong people who resisted the "Stockholm Syndrome," a phenomenon in which hostages sometimes develop affection for their captors.

"Our people baited the guards," he said. "There was no evidence of psychiatric capitulation. They made the best of their situation. They took a miserable, uncertain situation and got something out of it. . . . In some ways, it was not lost time for them."

Haynes cited the case of one hostage, a chain smoker, who feared that as punishment the Iranians would deny him cigarettes.

"So on his own, he just stopped smoking," Haynes said. "You could say he's a stronger person for what he achieved."