RICHMOND -- L. Douglas Wilder, much in demand for speeches as America's first elected black governor and perhaps setting up a run for national office, has quickly become the most traveled chief executive in Virginia history.

Wilder's travels began slowly. In his first six weeks in office, he made four out-of-state trips, three of them to the District. But since the legislature adjourned in mid-March, his out-of-state travel has increased in frequency and length, and the trips now number more than three dozen.

Although Wilder's immediate predecessors -- fellow Democrats Charles S. Robb, now a U.S. senator, and Gerald L. Baliles -- became globe-trotters during their years in the governor's mansion, both stayed closer to home in their first year in office. At this point in his administration four years ago, Baliles had made three out-of-state trips (he made eight in his first year).

But Wilder is widely sought out from around the nation and around the globe. He is accepting many of those invitations at the same time he faces a state budget shortfall of $350 million dollars back home.

He has yet to travel overseas as governor, but in a meeting Thursday with Prince Bandar bin Sultan bin Abdulaziz, Wilder told the Saudi Arabian ambassador that he will visit his nation next year. Wilder also plans to go to Japan, Taiwan and other Pacific Rim nations; Eastern Europe; and Africa. Invitations from Israel, Uganda, Angola, Nigeria and Tunisia are under consideration.

Wilder's hectic schedule -- this past week he spent Sunday night in Minneapolis; Monday, Tuesday and Wednesday nights in Washington; and Friday night in Des Moines -- is widely seen as an attempt by the governor to position himself for national office, in 1996 if not 1992.

Wilder contends that his frequent out-of-state trips are good for Virginia, that they boost pride back home and are an incentive for economic development.

At an impromptu news conference in Richmond on Thursday, the day before he left for two days of politicking with Democratic candidates in Iowa, Wilder said "no one has complained to me" about the travels. A spokesman for the governor said his office has received only one call complaining about his travels.

Wilder dismissed as "callous" a question about whether he is wasting taxpayers' money, and emphasized that he spends "about 18 hours a day, seven days a week" on state business. He cut short his Iowa trip to give the commencement address Saturday night to the Islamic Saudi Academy in Alexandria.

Wilder's dizzying pace continues next month with the governor's third trip to Los Angeles, where he will receive the NAACP's Spingarn Medal, and visits to Indianapolis for the Indiana Black Expo and to Memphis and Mobile, Ala., for conferences of governors.

Larry J. Sabato, a political science professor at the University of Virginia, called "wholly unbelievable" Wilder's contention that he is working night and day on state matters, but said there is "certainly no scandal" in his trips.

"Name me a major politician, when given the opportunity to get on a national ticket, who wouldn't jump for it," Sabato said.

Wilder is smart to make the most of his uniqueness now, Sabato added, because he could have competition on the national scene if gubernatorial candidates Andrew Young in Georgia and Dianne Feinstein in California are elected later this year.

Del. Alson H. Smith Jr. (Winchester), a Democratic fund-raiser who accompanied Wilder on one of his California trips, isn't concerned that the governor's travels will hurt his popularity. "The same stories were written about Chuck Robb and his national agenda," Smith said.

Wilder's press secretary, Laura Dillard, said the governor goes to great lengths to spend most weekdays in his office on the third floor of the Statehouse in Richmond. She emphasized that when Wilder went to New England earlier this month, for example, he flew black to Richmond, arriving about 1:30 in the morning, rather than stay overnight in New Hampshire, where he had made a political speech.

What she didn't make public, however, was that -- according to a logbook at the state Department of Aviation -- Wilder returned to New England the next day, using the state's jet, for a four-day stay on Nantucket Island.

Asked about that trip and an earlier one to Long Island, N.Y., neither of which appeared on the governor's public schedule, Dillard said Wilder has, or will, reimburse the state for the trips, which she described as personal.

Although Dillard said the governor has reimbursed the state for the Long Island trip, no record of payment was found at the state Department of Accounts.

Dillard said the governor's policy adviser, Walter A. McFarlane, determined early this year that it was "proper and appropriate" for Wilder to use state-owned aircraft for personal trips "if he cut a personal check" for them.

"When the trip is clearly political," Dillard said, "we can't use the state plane," or if the governor does, the sponsoring organization is supposed to reimburse the state.

Dillard said decisions on when to use the state plane are made by Wilder's chief of staff, J.T. Shropshire, appointments secretary Jacqueline Fritz and herself. According to records at the Department of Aviation, Wilder has used a state plane for 17 trips outside Virginia, and six in-state. On shorter trips, he often flies in state police helicopters.

Dillard said Wilder tries to use private planes, donated by supporters, for political trips. That's what he did this weekend in Iowa, with a plane supplied by Northern Virginia developer Al Dwoskin.

Such trips will be listed as political contributions on Wilder's next conflict-of-interest statement, Dillard said.

The state budget includes $52,920 (reduced from $55,000 as a result of the governor's order that state agencies cut their budgets 2 percent) for travel by the governor or his staff on planes operated by the Department of Aviation.

Wilder usually flies aboard the state's Cessna Citation S II, named "The New Dominion," a twin-engine, eight-passenger jet. His office is charged $585 an hour for flight time, plus expenses for the two pilots. When he uses either the older and slower King Air 200 or the Turbo Commander, both twin-turboprop planes, his office is charged $495 an hour.

Nearly all of the state police helicopter trips, for which the governor is not billed, are made on a four-passenger, twin-engine Bell 222.

"Not a week goes by that he doesn't fly with us," said state police Sgt. J.A. Nichols, one of the pilots who flies for Wilder.

This is a partial list of out-of-state trips made by Virginia Gov. L. Douglas Wilder since he took office Jan. 13. Unless otherwise noted, the trip was made on a state-owned airplane and paid for with state funds.

........................................................Air travel

Date............Place...............Purpose...................cost

Jan. 27.........Washington..........Speech -- National

....................................School Boards Assn........$546

Feb. 6*.........New York City.......Bloomingdale's promotion

....................................of Va. goods............$1,233

Feb. 24-27......Washington..........National Governors

....................................Conference..............$1,092

March 5-7**.....Long Island, N.Y....personal................$2,653

March 13-14***..Chicago.............Speach -- Illinois

....................................Democratic Party........$2,281

March 15-16.....Washington,New York.House Roads Committee

....................................and Sony .Awards........$1,802

March 23****....New Orleans.........Democratic Leadership

....................................Council.................$2,808

March 26-28.....Los Angeles.........Dinner.with

....................................Ronald Reagan

....................................and other events...........( )

March 31........Washington..........Gridiron Club dinner......$489

April 4.........Washington..........Two speeches............$1,014

April 7-8.......Los Angeles.........Speech -- California

....................................Democratic Party...........( )

April 28........Washington..........White House

....................................Correspondents Dinner.....$956

April 30****....New Haven, Conn.....Yale Political Union....$1,345

May 5-6****.....Atlanta.............Speech -- National

....................................Rainbow Coalition.......$1,936

May 21-22.......New York City.......Speech -- NAACP............$1,517

May 27..........Nashville...........Commencement -- Meharry

....................................Medical School..........$2,340

June 6..........Boston..............Commencement -- Harvard.......( )

June 6..........New Hampshire.......Political speech...........( )

June 7-10**.....Nantucket...........Personal................$3,707

June 17-18......Minneapolis.........Speech -- Hubert

....................................Humphrey Institute......$1,755

June 22-23......Iowa................Campaigning with

....................................Democratic nominees........( )

* Second plane for Virginia press provided by Larry Silver, of Fredericksburg.

** Governor personally will reimburse state.

*** State reimbursed $1,908.

**** Sponsoring organization will reimburse state.

( ) Plane arranged by Patricia Kluge, of Charlottesville.

( ) Plane arranged by former California governor Jerry Brown.

( ) Plane provided by T.A. Carter, Salem, Va., architect.

( ) Plane provided by Al Dwoskin, Fairfax developer.