Reagan's image in Europe does not help allies in deploying American missiles

This past week saw President Reagan take time out from fighting communism to try to patch up strained relations with friends and allies. He himself went to Japan where differences over trade have reached a critical point. He sent United States Deputy Secretary of State Kenneth Dam to Europe to try to mitigate disapproval among the NATO allies of the US adventure in Grenada.

The visit to Japan was the easier assignment. It had been well prepared.

Mr. Dam's mission to the NATO allies ran head-on into British Prime Minister Margaret Thatcher's outspoken and unabated disapproval both of what the President had done in Grenada and what a lot of Europeans thought he might be about to do next in Lebanon.

Reports of US naval forces concentrating off the Lebanese coast made the allies very anxious. The British, French, and Italians all made noises which suggested that if Mr. Reagan takes the military offensive in Lebanon, they might pull their own forces back out of the peacekeeping mission there.

Canadian Prime Minister Pierre Trudeau was also in West Europe during the week. His mission amounted almost to that of trying to mediate between the US and its allies.

The trouble is not so much that NATO leaders disapprove per se of the Grenada affair, but rather that it added to their own domestic political problems. Another US military offensive anywhere would further aggravate those problems.

Before Grenada, the NATO governments felt that they could handle their respective ''peace movements'' and could go ahead with the deployment of the new American nuclear missiles as planned. Grenada revived in Europe a public perception of Mr. Reagan as being ''trigger happy.'' Another US-initiated military event in Lebanon would greatly increase pressure on the NATO governments to call off the deployments.

The attitude of the European allies gives Mr. Reagan a difficult problem. The US Marines in Lebanon continue to take hostile fire and casualties. American public opinion dislikes the condition. Mr. Reagan would win more applause at home for sending the Marines forward to take up more defensible positions.

The Grenada affair was popular at home. This week the Democrats, led by House Speaker Thomas P. O'Neill, fell into line behind the President and gave their approval. It has proved to be a major political success for the President. He could, if he chose, do something else of like nature and be confident of general public support - provided, of course, that it would be as quickly and cheaply successful.

But what is popular in US politics can be political poison for allied governments in Europe. During the week the White House thought about all kinds of things it might do in Lebanon. A joint strike coordinated with Israel forces, aimed at Muslim Shiite positions, was on the list. At this writing, with the NATO allies shuddering and threatening to walk out, nothing had yet been done.

Relief for the Marines might be coming from a different source. Changes are taking place in Lebanon. The Palestine Liberation Organization forces loyal to Yasser Arafat were fighting their last battle near the Lebanese port city of Tripoli while the various Lebanese political factions negotiated in Geneva and returned home to Beirut.

Syria has obviously decided to drive out any PLO forces not willing to serve under Syrian command. And Syria has been dealing with Lebanese President Amin Gemayel. A ''deal'' seems to be in the making between Syria and Mr. Gemayel. The rough outline is believed to be that the Syrians will, in effect, keep Lebanon's mountain ranges, and ''the Great Valley'' which lies between, and leave to Mr. Gemayel and to the nominal government of Lebanon the coastal plain and the seaports.

Such a deal would mean leaving Israel with the southern strip it now controls including the ancient Phoenician seaports of Tyre and Sidon. But it would also mean shelving the agreement worked out between Israel and Mr. Gemayel earlier. Israel would keep its buffer zone in southern Lebanon, but it would not get the political and economic entrance into Lebanon which was contemplated in the agreement. In the event of such an arrangement, the fighting might largely end and the Marines could go home.

Meanwhile, foreign offices around the world had a new task this week. They had to bring out their files on the Soviet leadership and try to guess what seems likely to come next in the Kremlin. Soviet leader Yuri Andropov had failed to take his place on the roof of Lenin's tomb for the usual annual military parade in Red Square. That had not happened before. The assumption was that the Andropov tour of duty at the Kremlin is likely to be short. Will the next man at the top be another elderly member of the old guard, or one of the new generation - which always seems to be just around the corner of Soviet politics?

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