Another tumultuously busy weekend for Europe's antinuclear protesters underlines the need for greater American understanding of West European nuclear fears.
It also shows the dangers for the West of failing to counter effectively Soviet exploitation of the wave of anxiety rippling across Europe.
The 150,000-strong turnout of protesters in London Oct. 24 was described as the biggest demonstration ever seen in the British capital. There was a roughly similar turnout in Rome the same day. And 24 hours later, it was the turn of Paris and Brussels.
Two weeks ago, a quarter-million protesters crowded into Bonn, the West German capital. Antinuclear groups plan a demonstration in Amsterdam for Nov. 21 . And there will be a ''joint action'' demonstration in Brussels during the NATO council meeting there in December.
It is a NATO decision of 1979 that the demonstrators are trying to get reversed: to install US cruise and Pershing II missiles in the European theater by 1983.
What makes their aim so politically sensitive is that it coincides with the Soviet determination to prevent the planned introduction of the missiles into Western Europe.
The Soviet motivation is self-evident. Cruise and Pershing II missiles would rob Moscow of the nuclear advantage it has now in Europe with its SS-20 missiles , for which NATO has had, until now, no counter.
Does this coincidence of the Soviets' and the protesters' aims mean the bulk of the latter are communists?
No - no more than the bulk of the antinuclear protesters at the Diablo Canyon , Calif., or Seabrook, N.H., plants are communists. Or for that matter, no more than are President Reagan's friends in Nevada and Utah who opposed the siting of MX missiles in their states.
Few people want nuclear installations, let alone nuclear weapons, set up in their backyard. They know that in the event of war, those weapons become a prime target of the other side.
But there is a world of difference between the consequences of contemporary antinuclear protest in the US and in Europe. In the US, it has little impact on the deterrent effect of the nuclear balance.
In Europe, it opens up the chilling prospect for NATO of, first, a major breach between the two sides of the Atlantic, and then of the neutralization of Western Europe under the permanent threat of Soviet nuclear superiority.
Nothing could suit Moscow's purposes better. It is what the Kremlin has wanted ever since the end of World War II.
The Soviets are, in fact, unabashedly encouraging the fears of those Europeans worried that the introduction of US theater nuclear weapons on their soil means that American strategy is to fight any nuclear war ''to the last European'' and spare the US from Soviet long-range nuclear attack.
Britain had its antinuclear campaign in the 1960s, led by the left. It was stopped in its tracks by the tireless and courageous efforts of the late Hugh Gaitskell, then leader of the Labour Party.
This time round, 20 years later, the present Labour leader, Michael Foot - in theory Britain's alternative prime minister to Margaret Thatcher - is egging the protesters on. He proudly boasts of being a ''peacemonger'' and calls for unilateral nuclear disarmament by Britain.
But the growing strength of Britain's new alternative Social Democratic Party , which opposes unilateral nuclear disarmament, lessens the likelihood of Mr. Foot's accession to the premiership.
In fact, the dimension of the protest in Britain is probably of less concern to the alliance as a whole than is the breadth of the sweep of the antinuclear movement in West Germany. There it includes respected members of the Protestant clergy and members of Chancellor Helmut Schmidt's own Social Democratic Party.
The biggest single victory of all for Moscow would be to force Mr. Schmidt to reverse his 1979 decision to accept cruise and Pershing II missiles.
At that time, Mr. Schmidt made West Germany's acceptance of the missiles conditional on at least one other mainland European country's agreeing to their installation. Italy said ''yes,'' Belgium and the Netherlands ''perhaps.'' Since then, internal political developments in Belgium and the Netherlands have made it increasingly likely that ''perhaps'' will become ''no.''
Hence the heightened importance of Italy in the nuclear debate - and the significance of the Oct. 24 protest demonstration in Rome against the missiles.
The challenge to the US and pro-missile European government officials is sensitive, even baffling. To dismiss the protesters as ''reds'' or ''dupes'' tends to be counterproductive. Patient education, even at this late date, seems a more fruitful course.
So it is interesting to note that two of the State Department's top experts with European experience - Walter J. Stoessel Jr. and Lawrence S. Eagleburger - were in Europe at the weekend. Mr. Stoessel was quoted as saying the protest movement must be taken seriously. And the tenor of both men's remarks on the movement could be described as educational.