While the Carter administration wrestles with Israeli concerns about an unauthorized meeting between former U.N. ambassador Andrew Young and a representative of the Palestine Liberation Organization, the West German government is trying to get out from under a similar situation that has unfolded here in recent days.

Bonn's problem grew out of a meeting in Beirut last week between PLO chief Yasser Arafat and 34-year-old Juergen Moelleman, a member of Parliament and the chairman of the Foreign Policy Committee of the Free Democratic Party. The Free Democrats are the small but crucially important coalition party to the ruling Social Democrats in Bonn's federal government. The leader of the Free Democrats, Hans-Dietrich Genscher, is also West Germany's foreign minister.

Because of this, Moelleman's journey was bound to take on some symbolic importance and before he left, the young parliamentarian -- who is something of a Genscher protege -- met with Genscher and talked of the minister's "full cooperation." The trip, however, has produced considerable confusion and big headlines during an otherwise sleepy Bonn August, and has added further to suspicions in Israel that Bonn's foreign policy toward the Jewish state and the Middle East is shifting.

The Israelis were particularly concerned because Moelleman's journey came slightly more than a month after former West German chancellor Willy Brandt, acting in his capacity as head of the Socialist. International, and Austrian Chancellor Bruno Kreisky met with Arafat in Vienna.

Israeli opposition leader Shimon Peres told a West German magazine this week that both the Brandt and Molleman meetings, filled Israelis with deep forebodings.

During his talks, Moelleman presented Arafat with a position paper that supposedly outlined West Germany's policy on the Middle East situation.

Press reports from Beirut, however, indicated that Moelleman actually presented a "eight-point peace plan," which contained two items that seemed to go beyond Bonn's public policy. One involved a more detailed suggestion that Israel revert to its pre-1967 borders and the other spoke, for the first time, of a "state organization" for the Palestinians, which seemed to go beyond the more widely accepted European view of the right of self-determination.

The Beirut accounts caused an explosive reaction here. Genscher, the Free Democratic Party and the federal government quickly disassociated themselves from Moelleman's venture and reported ideas. The foreign ministry was particularly annoyed.

Moelleman claims that he was victimized by poor press reports. He says he presented no peace plan and that there was no question of him being a special emissary who was paving the way for recognition of the PLO by Bonn. The Israelis greatly fear Western recognition of the PLO.

The opposition Christian Democrats have criticized sharply the Moelleman visit, calling him "an amateur playing with a powder keg," warning that such adventures were damaging West Germany's relations with Israel and even other Arab countries, and demanding that the government "either bring to an end, or bring under control, the escapades of this junior politician."

Yesterday, however, a former minister for development aid in the current Social Democratic government, Marie Schlei, supported continuing contacts between West German parliamentarians and the PLO. Writing in the party newspaper Vorwaerts, she said such contacts, aimed only at getting the PLO to take a peaceful road and away from their aim of destroying Israel, were in Israel's long-term interest.