President Bush's far-flung coalition against Saddam Hussein is threatened by strains, so far most evident in France and Egypt, that are certain to get worse in the difficult months ahead.

These strains, dubbed "coalitionitis" by an administration insider, stem from internal politics in the allied countries -- not from disaffection with Bush's alliance. In France, it is French pride that is as old as the country itself. In Egypt, radical dissidents and anti-Israel politicians abhor the prospect of fighting an Arab state under the American flag.

The danger is heightened by a new consensus inside the administration: that the real pain of U.N. sanctions will not be felt in Baghdad until next spring ("not till the second quarter," a middle-level diplomat confided). If sanctions are to get a fair chance to succeed, that means the president faces a much longer no-war, no-peace twilight than imagined when he rushed troops to the Gulf nearly three months ago. The longer the wait, the worse the disease.

In France, President Francois Mitterrand, a strong supporter of Bush's anti-Saddam policy despite historic French ties to Iraq, came under sudden attack this month. Jacques Chirac, the mayor of Paris and conservative leader in the French Assembly, asked Mitterrand whether the 5,000 French forces now in Saudi Arabia could be taken into battle against Iraq by the United Nations or the United States, and if so, who would command them.

Mitterrand promised that France would maintain "complete autonomy" over its own forces. Chirac responded that would be very difficult to do if hostilities are launched "that we ourselves did not decide." That is the prelude to what could become a rancorous political debate in France, now that Mitterrand has tied his prestige to the made-in-Washington U.N. policy to force Saddam out of Kuwait.

"Chirac has decided to lead the charge against Mitterrand for being too close to the United States," a high Bush administration official told us. The political necessity of maintaining a policy a few degrees removed from Bush's could induce Mitterrand to give Saddam far more leverage in meeting U.N. demands than Bush will accept.

In Egypt, coalition trouble is more visible and dangerous. Its first, murderous symptom was the assassination of the Assembly Speaker Rifat el-aghoub, second-ranking official after President Hosni Mubarak. Few Western politicians can believe the Egyptian officials who say the killing had nothing to do with supporting the United States against Saddam.

But there was no doubt about motive when Maj. Gen. Mohammed Ali Belal told reporters Egyptian forces under his command were in the Gulf only to defend Saudi Arabia, not to attack Iraqi forces and free Kuwait. That tarnished the very heart of the coalition idea and produced a strong, unpublicized complaint from the Bush administration. Bush wants Arab troops as political cover for Americans if the first-ever American war against Arabs starts.

The United States has high cards to play in dealing with Egypt, including Mubarak's dependence on economic help and the forgiveness of Cairo's $7 billion debt to the United States. Shortly after the complaint, State Department officials said privately that the Egyptian general had been fired for "talking out of turn." Arab diplomats confirm he has been reassigned to Cairo.

Sentiments of Arab coalition members help explain the heavy U.S. pressure on Israel to stop killing and abusing Palestinians and to end the settling of Jewish immigrants in Jerusalem. But the White House is not confident that it can alter the Israeli conduct that infuriates Arab coalition partners.

"Coalitionitis" afflicts Damascus and Moscow as well. The CIA is studying credible reports that Syrian President Hafez Assad's decision to send Syrian troops to join the coalition is causing serious political repercussions that might even produce an army-led revolt. Soviet President Mikhail Gorbachev swears fidelity to Bush and the United Nations, but the American president's key advisers believe that he will do what he can to block the United States from gaining Persian Gulf hegemony.

This suggests that time may not be an ally as the sanctions noose tightens around Saddam. Time may prove to be the opposite as strains within the coalition threaten to pull it apart.