The NATO alliance was shaken and damaged this past week both by what the United States did in Grenada and by what the European allies did about it. The allies disliked the use of American troops in Grenada - and they said so, loud and clear.
Not a single ally spoke out in official approval either of the American deed or the reasons advanced by the President of the United States for it. He, in turn, was startled and shaken by their unanimous lack of vigorous support and approval.
The immediate effect was to undermine the stiffening of the alliance that had resulted from the Soviet shooting down of the South Korean airliner.
The US had gained the diplomatic initiative because of that Soviet act of brutality and new American flexibility in the nuclear arms talks. Through September and October the effects were seen in the weakening of Europe's ''peace movement.'' It was largely paralyzed. Western European governments looked forward with equanimity to the arrival in December of the first of the new American nuclear weapons.
But October ended with the initiative back in Soviet hands and the West European governments having to revive their plans for handling those peace demonstrations which are expectable now in more vigorous form when the weapons begin to arrive.
If the lack of European sympathy seemed out of proportion to the seizure of Grenada and the nature of the case, there is a reason. The allies were reacting not just to a quick and decisive use of force. Their reaction was symptomatic of an underlying growing distrust of US leadership in the alliance.
Grenada is a small island with only a little over 100,000 people. Its leadership had fallen into bloodied Marxist hands. Cuban intrusion was unmistakable. Probably most leaders in most of the allied and friendly countries were privately relieved to know that Fidel Castro is not going to be able to add Grenada to his mini-empire.
But the US President based his case largely on anticommunism and presented it as an issue in East-West relations. British Prime Minister Margaret Thatcher, speaking on a BBC program, said she is ''utterly against communism and terrorism'' but could not go along with ''a new law that wherever communism reigns against the will of the people . . . the United States shall enter.''
A British diplomat, speaking of differences in perception on opposite sides of the Atlantic about Western defense and NATO, put the matter this way:
''European members of NATO believe that the Reagan administration sees NATO and Western defense as being directed 'against' the Soviet Union. Britain and the European members would see it slightly differently: that NATO exists so that we may live with the Soviet Union in security.''
In other words, the allies want no part of any policy aimed at breaking up the Soviet empire or bringing down the present Soviet government. They tended to see in the invasion of Grenada an unnecessary overreaction with overtones of a forward and aggressive strategy.
Mrs. Thatcher told Parliament she felt the problem in Grenada could have been handled through a combination of diplomacy and economics.
President Reagan was obviously surprised and hurt that Mrs. Thatcher had not come to his support and defense, since he had so recently supported her in Britain's recapture of the Falkland Islands. But his surprise overlooks the fact that the West Europeans live next door to the Soviets and would presumably be a main battlefield in any war.
NATO has recovered from previous crises of a similar nature and presumably will recover from this week's damage. If constitutional government is restored promptly in Grenada and if US troops finish their work and go home promptly - this particular crisis can end up largely as a short-term propaganda gain for the Soviets comparable to the gain the US scored when the Soviets shot down the Korean airliner.
The Korean airliner deed made the Soviets appear to be the more warlike and trigger-happy of the two superpowers. The use of US force in Grenada pinned the ''trigger-happy'' label back on the US - in European eyes.
The underlying uneasiness that caused the Europeans to overreact (underreact in Reagan eyes) to the Grenada invasion is another matter that will call for long-term treatment.