For the Bush administration, worried about maintaining international backing for military action against Iraq, the challenge to Prime Minister Margaret Thatcher's leadership of Britain's Conservative Party could not have come at a worse time.

Administration officials and outside experts said they were not concerned that a successor to Thatcher would alter Britain's support in the Persian Gulf. Nor is there substantial worry that a British move toward closer economic union with the European Community -- a move Thatcher opposes -- would hurt U.S. interests, they said.

The concern is that even if Thatcher wins today's Tory party leadership vote in London and remains as prime minister, as seems likely, Iraqi President Saddam Hussein might perceive her problems as a weakening of America's most steadfast European ally.

"This is the wrong time for this {challenge}," an administration official said. "This is a time when you want as few variables . . . varying. It may have no effect {on the gulf situation} but it may have an effect."

"This is not to say that a successor would not be equally supportive, but it would be hard to find someone more supportive. You cannot imagine . . . the importance of being able to know that you can count on an ally {like Thatcher} without the hesitations and the headaches" that sometimes arise even from consultations among friends, the official said.

There are two possible successors to Thatcher. Former defense secretary Michael Heseltine has directly challenged her in today's party vote. Unless Thatcher wins by a large majority, they could be forced into a second round in which Foreign Secretary Douglas Hurd is viewed as a possible compromise candidate. Both men are considered virtually certain to continue Thatcher's policies in the gulf. But experts and administration officials agreed it would not be the same as having Thatcher herself in office.

"If you're trying to persuade some thug {like Saddam} to leave," said Michael Mandelbaum, a professor at the Johns Hopkins University's School of Advanced International Studies, the British party vote itself may affect the gulf situation "to the extent that the coalition seems less solid or that one of the senior partners may be weakened."

If Hurd or Heseltine were to succeed Thatcher as head of the party -- automatically becoming prime minister -- Britain's "positions won't change on the gulf, but there won't be the same summoning trumpet emanating from London," Mandelbaum said.

If the crisis in the gulf "comes down to the question of 'go or no go,' " he said, Bush will not want to be alone. "If he calls, she would say 'Go, and we're ready.' But a successor may not, or may not do so in the same way." Heseltine or Hurd might be concerned about how such a decision would affect his chances in Britain's next general election, which must be held by summer 1992, Mandelbaum said.

Thatcher has been if anything ahead of Bush in terms of favoring prompt military action against Iraq. Her presence and position on that offer Bush strong "emotional support," the administration official said. While the other Conservatives, and even opposition Labor Party leader Neil Kinnock, could prove equally supportive, "for foreign affairs, {the administration} couldn't find anyone better," he said.

Bush has not forged the close personal bond with Thatcher that characterized then-President Ronald Reagan's relationship with her. For much of his administration, Bush has seen a united Germany as the driving force in Europe and has focused much of his energy on improving his ties to German Chancellor Helmut Kohl.

Iraq's Aug. 2 invasion of Kuwait has slightly altered that equation, with Britain again laying claim to its traditional "special relationship" with the United States and Germany faltering in its support for U.S. policies in the gulf.

Ironically, the issue that sparked this most serious challenge to Thatcher's 11 years as prime minister -- the question of Britain's role in Europe -- is the one major area where the Bush administration differs with her.

"Our government has become uncomfortable with Thatcher's position vis-a-vis Europe because we feel she could have a positive position," said Helmut Sonnenfeldt, a guest scholar with the Brookings Institution.

"All in all, our government thinks that the British would be better off participating in the European process," he said. "We still have a view that the British are more internationalist inclined" toward the rest of the world than others in Europe, and this "would help raise the horizons of the others" on the continent.