The U.S. Department of Energy is investigating the unusual circumstances surrounding an official working trip to Alaska and Canada made at government expense by the stepson of a top department official.

The trip was made in late May and early June by Jonathan Willens, a college student who is the stepson of Deanne C. Siemer, special assistant to Energy Secretary Charles W. Duncan Jr. As Duncan's chief of staff, Siemer is one of the cabinet officer's top advisers on policy issues.

When Duncan first heard about the 10-day trip -- while Willens was still away -- he angrily ordered that Willens have no more official relationship with the department, according to Duncan's top spokesman, Lee Daly.

The department paid an $807.23 air ticket for Willens but is holding up payment on $937.80 in expenses while the investigation by the department's inspector general is under way. Willens was unsalaried while working for the department, Daly said.

"Duncan acted immediately because it had the appearance of an impropriety," the energy secretary's counsel Michael Kelly, said yesterday.

Duncan declined to comment yesterday, saying through Kelly that it would be inappropriate to comment before the investigation is complete.

Siemer left on a long vacation in Europe shortly after Willens returned from the trip in early June. Repeated attempts by The Washington Post to reach her through her secretary failed over several days.

Attempts to reach Willens at his father's house in Northwest Washington also failed, although friends there said he is in Washington.

At the time Duncan acted, the inspector general, an independent policing official inside the Energy Department, was already investigating the trip. The investigation will determine whether the trip was legal.

Daly, the public affairs man, said Willens made the trip with a government employe to perform official advance work for a three-day trip that Duncan will make next week.

Daly said that Willens was not on the department's payroll or on the payroll of any consultant to the department when he made the trip.

He said that Siemer ordered him to saign "invitational travel orders" that authorized Willens -- a private citizen -- to travel at government expense.

"I agreed that it should be signed because Deanne Seimer instructed me to," Daly said yesterday. "I was advised that it was legal by Deanne Siemer."

Before being brought by Duncan to the Energy Department last summer, Siemer was the general last summer, Siemer was the general counsel of the U.S. Department of Defense, a presidential appointment. The power of her office and her strong personality led some critics to refer to her as a "dragan lady."

Duncan was then deputy secretary of defense, a post he left when President Carter made him energy secretary last Aug. 24.

Energy Department officials described Willens as bright and hardworking and at no time did they suggest that he had done anything improper or illegal himself.

According to Energy Department officials, Willens is the son of Howard P. Willens, an attorney in the Washington law firm of Wilmer & Pickering -- the same firm of which his wife, Deanne Siemer, was a member before going to the Defense Department in 1977.

Howard Willens' secretary said yesterday he is traveling in Italy with Siemer and could not be reached for comment.

A spokesman for the U.S. General Services Adminstration said yesterday that "invitational travel orders" are customarily used to authorize travel expense payments to persons who travel on official government business but who are not on the government payroll.

For example, expert witneses in trails and potential government appointees travel on such orders, the spokesman said.

He said that whether use of orders in the Willens case was proper would depend on the rules and procedures of each individual government agency -- in the Willens case, the Energy Department.

A DOE spokesman refused to say yesterday what the department's rules are in such matters, citing the ongoing investigation.

Daly said yesterday that Siemer's command to him to sign the travel orders was not the first time he had heard of Jonanthan Willens. Earlier, he said Seimer had asked him to employ her stepson as a summer intern in the department's public affairs office, which Daly runs.

"The first idea was she wanted him to work in the department. I interviewed him. . . . She brought him in to be interviewed. I thought he was a decent kid. He filled out an application," Daly said.

But Daly didn't have any jobs available, and told Siemer so. He said she persisted in trying to get Daly to hire the youth, but he was adamant that he didn't have the slots.

"That's the last I heard of it until he turned up on this travel thing," Daly said.

After Daly interviewed him for a job, the youth worked for several days -- May 19 through 23 -- for a small engineering consulting firm in Columbia, Md., called AMAF Industries Inc., according to AMAF President Robert L. Jones.

Jones said the firm has a small DOE contract but that Willens did not work on that. Rather, Willens did technical writing on other contracts, Jones said.

Jones could not recall how the youth happened to come to work for AMAF. "He probably was referred to us. . . . It might have been someone down at DOE who referred [him to] us. I get 15 calls every summer wanting to get jobs for kids," Jones said.

Then abruptly on May 23 Willens quit, giving no explanation, Jones said.

The next day, May 24, Willens left for Alaska and Canada, according to Hank Greely, an aide to Siemer who was the official advance man for Duncan's trip.

Greely said that he and Willens traveled together to several Alaskan cities and then to Alberta, Canada to perform the advance work.

The work involved such things as making hotel reservations and obtaining the measurements of airport runways so that the energy secretary's trip would go smoothly. The two also interviewed local officials and interest groups to get a political reading for Duncan on what to expect.

"Jonathan basically was up there as my assistant," Greely said. "He was an extra pair of eyes, arms and legs for me. . . . It's not a trip that I would have wanted to do by myself. He took notes, made phone calls to set up things. . . . He did cover one meeting for me with environmentalists in Anchorage when I couldn't make it."

Greeley described Willens as "hard working . . . intelligent . . . very helpful."

After the trip, Willens turned in his reports and notes, then was not seen again at the Energy Department, Daly said.

Duncan will leave on his trip to Alaska and Alberta Tuesday, Daly said. The energy secretary will focus on energy development in Alaska and supplies from Canada of oil and natural gas.