LONDON, JAN. 17 -- British officials expressed cautious optimism today over the apparent initial success of the multinational air offensive against Iraq, while the French described their pilots' entry into the campaign with attacks on Iraqi-occupied Kuwait.

Prime Minister John Major told the House of Commons: "Iraq does have a very substantial number of men under arms. They have very sophisticated weapons, and in many cases they have a considerable degree of hardened military experience. There is a great deal left to be done before this matter is resolved. . . . We cannot yet say that there is command of the air."

Officials confirmed, meanwhile, that two British Tornado fighter-bombers were lost, one when its engine caught fire during the second wave of attacks this morning. Defense Secretary Tom King said it was unclear whether the fire was caused by Iraqi air defenses or a malfunction. The two-man crew parachuted at an undisclosed desert location, and officials said attempts were being made to rescue them. The second plane was lost tonight, but no details were available.

Major's caution reflected the fears of officials here that early popular euphoria could mislead British and American public opinion into believing the conflict could be swift and painless, according to government sources. They fear the reaction could swiftly turn negative if allied forces suffered major losses.

In Paris, Defense Minister Jean-Pierre Chevenement said French warplanes were sent into battle in the second wave of allied air assaults, attacking Iraqi positions at Jabir airport, south of Kuwait City.

The 12 Jaguar fighter-bombers returned to base safely, although four were hit by antiaircraft fire and one pilot was slightly injured, Washington Post Paris correspondent William Drozdiak reported. Chevenement said that the planes damaged "a good number of their objectives, notably hangars that shelter planes and helicopters, ammunition depots and ground-to-air missile batteries."

British defense secretary King told reporters that while the international forces had made "a very encouraging start," Iraqis had attempted in recent days to disperse aircraft, making them less likely to be destroyed on the ground. "They may well be conserving the resources they have," warned King. "I wouldn't want people to jump to early conclusions."

Waves of British Tornadoes based in eastern Saudi Arabia and Bahrain hit Iraqi airfields and air defense installations throughout the night and day. The planes used several sophisticated new British-made weapons never seen on the battlefield before, according to defense officials here.

Tonight, defense officials reported that British Jaguar fighter-bombers had begun air raids against Iraqi military positions inside Kuwait. King confirmed that some of the British attacks had been aimed at Iraqi Republican Guard units that are the elite of Baghdad's ground forces.

The public here heard some of the same first-person broadcast accounts of the air raids on Baghdad as did television viewers in the United States. BBC reporter John Simpson described seeing a U.S. cruise missile whiz by his fifth-floor hotel window at daybreak. "It just went straight down the road," he said. "Where it was aimed for, I just don't know."

Part of the government's caution, analysts said, stemmed from the fact that officials would not receive accurate intelligence assessments of the first day's damage until Friday morning. And part stemmed from the nagging fear that Iraqi President Saddam Hussein could be holding back and protecting many of his most important military assets.

Britain has about 35,000 military personnel deployed in the Persian Gulf, the second largest Western contingent. Officials here who have sought to portray London as Washington's closest and most dependable ally in the crisis said Major and President Bush first agreed on an attack soon after the Jan. 15 deadline during a 90-minute car ride to Camp David on Dec. 21, during Major's visit to Washington.

They said Bush informed Major Tuesday night during a 20-minute phone conversation that the attack would begin the following night. The two leaders spoke again this afternoon and reportedly agreed to portray progress of the offensive in a cautious light.

While Major sounded a low-key note, others here were more bellicose. "Many of us are very relieved that we are now fighting back," said former prime minister Margaret Thatcher. "The fact is the war started the day that Saddam Hussein marched into Kuwait. {He} has treated those people brutally, and so far they've had no one to fight back for them. Now they know we are fighting back in no uncertain way."

Drozdiak added from Paris:

Defense Minister Chevenement said satellite reconnaissance photos indicated that the most important accomplishment of the French air attacks was the destruction of all fixed antiaircraft SAM-6 and SAM-8 missile sites. He said French pilots were surprised by the weak resistance from the Iraqi air force, which sent only about 20 planes into the air against them. Two Iraqi planes were shot down, he said.

Successive air attacks will be aimed at destroying the fighting capability of the Republican Guard, Iraq's most disciplined and politically reliable forces, Chevenement added.

Chevenement said France had reached a clear understanding with the Americans that its air, ground and naval forces would not become involved in attacks on Iraqi territory but would limit military operations to the liberation of Kuwait, although he acknowledged that some of those engagements might spill into Iraqi territory.

A protocol was signed between the United States and France just before the war broke out specifying that France's independent military forces would be placed under American command for "predetermined missions" inside Kuwait. For that reason, French military sources said, French planes did not participate in the first massive wave of bombings by U.S. and British planes.