All three European countries with troops in Lebanon would like to pull them out. But for the moment, neither Paris, Rome, nor London knows how to do so without leading to even worse fighting and loss of life. Worried and pessimistic about the tortuous search for a political solution in Lebanon, they hang on and look to President Reagan for a lead.
All three would like to shift the responsibility for peacekeeping to the United Nations. But they realize that the idea has little support in general, and is opposed by Syria and Israel, plus the Soviet Union, which could veto such a step in the Security Council.
Already France has said it plans to redeploy 482 of its 2,000 Beirut-based troops to southern Lebanon, where they will join the UN force there.
The Italian government is discussing a plan to pull out half of the 2,200 troops it has in Beirut.
Although the British government is leaving its small but highly visible group of 110 troops in place for the moment, sources close to the foreign office say Prime Minister Margaret Thatcher would very much like to withdraw if she could find a way that would avoid more killing.
Talks with officials in all three capitals reveal a gloomy mood, in contrast to rising American optimism that newspapers here say is appearing in Washington.
Europeans see the release of Lt. Robert Goodman as yet another Syrian effort to get United States forces out of Beirut. They think much more political spadework needs to be done before softer Reagan rhetoric about Syria could lead to real progress.
One hope is that a Lebanese plan to create buffer zones between warring factions might come into force. Any such move would make it easier for European governments to defend their troops' presence in Lebanon.
''The trouble is,'' says one British official, ''that there's little sign of an adequate political framework within which the peacekeeping force can operate. The tripartite talks which began in Geneva in December have no date to resume. Those talks are extremely important.
''Besides, someone will have to give the Syrians something to get them to cooperate - besides Israel out of Lebanon, what do the Syrians really want? US pressure on Israel to give back the Golan Heights?''
The official shrugged. The Golan Heights are firmly in Israeli hands.
Domestic pressure is rising in all three European capitals to pull out. Sources ask how long it can be resisted.
French officials mask their distress by saying that if their 482 troops go back to southern Lebanon, they will still have the number of peacekeeping soldiers they originally committed. France's mission, the officials say, has not changed. In Rome, Defense Minister Giovanni Spadolini has repeated his view that the Italian contingent has won the nation prestige and respect.
Nonetheless, President Sandro Pertini on New Year's Day said Italian troops should stay only if they can contribute to a genuine peace. If not, only an Italian field hospital should be allowed to remain in Beirut. So far one Italian has been killed and 45 wounded.
In London, opposition Labour leader Neil Kinnock favors withdrawal. Mrs. Thatcher holds him at bay with her huge majority in the House of Commons, and the lack of British casualties so far.
''If we lose some men,'' comments one government official, ''then the uproar will really begin.''
Mrs. Thatcher has just said that ''alternative arrangements'' must be made before peacekeeping forces can leave. The ''obvious thing'' is an expanded role for the United Nations.
Officials were upset by the three days of fighting that broke out when France handed back two key positions to the Lebanese Army just before Christmas.
Their dilemma now is to offset domestic criticism without being seen as fanning the flames of war.