The West's hidden summit at Bohemian Grove

Europe is the main arena where the struggle between the two nuclear superpowers - the United States and the Soviet Union - is being played out, just as it was when NATO was established three decades ago.

This, despite such awesome diversions as the two current wars in the Middle East with all their savage destruction and human suffering. A cautious, conservative, aging Soviet leadership seems capable of little more in the Middle East than waiting for some development to exploit to its advantage, and the disadvantage of the US.

But in Europe, Soviet President Leonid Brezhnev has a carefully devised plan and timetable: to thwart if humanly possible NATO's deployment in Europe next year of cruise and Pershing II missiles, which would offset the present advantage Moscow's SS-20 missiles give it in European nuclear weaponry.

Against this background, ''Atlanticists'' in both the US and Europe deplore what many of them feel is the sourness and disarray that have increased between Washington and its West European allies since President Reagan entered the White House. This, they argue, works only to the advantage of the Soviets.

There are three immediate major areas of friction between the two wings of the alliance:

1. US efforts to put a brake on West European cooperation with Moscow in building the gas pipeline from Siberia to Western Europe.

2. An incipient trade war over the export of European steel to the US.

3. High US interest rates, which attract European money away from Europe unless the Europeans put their own rates up - which in turn sends European unemployment soaring.

During the past week there has been under way a most significant fence-mending effort by West German Chancellor Helmut Schmidt and George P. Shultz, the new US secretary of state, to keep transatlantic recriminations under control.

On July 20, Mr. Schmidt, avoiding New York and Washington, flew quietly into Houston for what was described as a lecture tour and working holiday. The next day he flew to California to be the house guest of Mr. Shultz for two nights at the latter's Palo Alto home.

From there, Mr. Schmidt went up to the redwoods 60 miles north of San Francisco to be Mr. Shultz's guest for two nights at the Bohemian Grove, an exclusive resort and retreat for wealthy businessmen. Defense Secretary Caspar Weinberger and former Secretary of State Henry Kissinger were scheduled to join them there.

Mr. Weinberger's presence makes it certain the question of the cruise and Pershing II missiles will be touched on. But, for the moment, it is not an issue that divides the allies - certainly not Americans and Germans.

The US and the USSR are engaged in negotiations in Geneva aimed at some measure of control of nuclear weapons, including those within the European theater of NATO. If there is not substantial progress in this aspect of the Geneva talks, the cruise and Pershing II missiles will be deployed - mainly in West Germany. Mr. Schmidt has in effect staked his political future on that.

The Bohemian Grove talks were expected to deal principally with sweetening the atmosphere generally between the US and its European allies - with little expectation that Washington will radically change its stance on either the pipeline or steel exports.

West Germany is less affected by the steel ''war'' than other European allies , and the inclination as the talks started was to leave interest rates on the back burner.

Mr. Schmidt and Mr. Shultz were therefore expected to concentrate on finding a way to agree to disagree civilly on the pipeline question that would leave little or no opening for Mr. Brezhnev to exploit to Soviet advantage. While in Houston Mr. Schmidt made clear that West Germany stood by its commitment to go ahead with the pipeline.

Earlier this month, two members of the European Commission (EC), Viscount Davignon of Belgium and Wilhelm Hafer-kampf of West Germany, were in Washington to ask the Reagan administration to be more flexible on both the pipeline and steel. They did not succeed in softening the US attitude.

On the pipeline - and other issues where the US is hard-nosed toward the Russians - there is a rationale for the US attitude, even if European critics see it as too confrontational.

Ronald Reagan's victory in the 1980 presidential election was due partly to a swing in the US national mood toward a tougher policy in dealing with Moscow. Some identified Mr. Reagan's own approach as that of a particularly Californian type of US nationalism. In any case, that approach is less confrontational than it is keeping the pressure up on the Russians in areas where they are weak.

The constraints the US government has sought to put on any Western cooperation with Moscow over the pipeline are directly connected with the jam in which the Russians find themselves over Poland. If only Polish leader Wojciech Jaruzelski lifted martial law, it has been mooted in Washington, there might be some ''give'' in the US position. It remains to be seen whether the equivocal liberalization measures - stopping short of lifting martial law - announced by General Jaruzelski July 21 offer any opening in this direction.

In the meantime, the Europeans insist they will defy any attempt by the US to force European subsidiaries of American firms to break contracts already signed for the supply of pipeline equipment. French Prime Minister Pierre Mauroy reaffirmed July 22 that this would indeed be the French stand.

Why, the Europeans ask Washington, do you expect us to imperil our trading reputation when you Americans - for domestic political reasons - refuse to put the squeeze on the Russians with a grain embargo, which would hurt far more than any ban on pipeline supplies?