How great a role do communists in general and the Soviet Union in particular have in West Europe's antinuclear movement? Few West Europeans would go along with President Reagan's assertion that the peace movement here is largely sponsored by the Soviet Union. (His comments are part of an interview taped Dec. 16 for the Public Broadcast Service program ''Ben Wattenberg At Large,'' scheduled to be aired Dec. 25 in the United States.)
A spokesman for the Campaign for Nuclear Disarmament in England has protested Reagan's dismissal of the various grass-roots antinuclear organizations that have mushroomed in Europe in the past year as creatures of the communists. And West German antinuclear leaders contacted by phone strongly rejected the view that their groups are steered by communists.
''It's not true,'' said Ulrich Frey of the Bonn Action Society Service for Peace, when asked about Reagan's charge. He hadn't previously heard of Reagan's remarks, but he is involved in preparing the written answer of his organization to a query about communist influence on antinuclear movements made by conservative members of Parliament in the West German Bundestag. The Action Society Service for Peace was one of the main organizers of the 250,000 strong antinuclear demonstration in Bonn last October.
In elaborating on his reply, Frey noted that there are many quite different groups involved in antinuclear protests in West Germany. They do include communists - and the West German communists are ideologically orthodox and loyal to Moscow - but the communists are a very minor part either of the West German political scene or of the antinuclear protests.
''We are not so blind as to say that when the German Communist Party works with us it is doing so in a Western democratic sense,'' Frey observed. ''In Moscow no demonstrations can be made. In East Berlin no demonstrations can be made.'' The communists have their own aims, of course - but Frey's and other Christian peace organizations do not for that reason shut out communists, he said. As Christians, they are especially careful not to form an ''enemy image'' of anyone. (The East German Lutheran Church also insists on this point, for example, in opposing portrayal of Western nations as enemies in East German schools.)
Western intelligence organizations go further than Frey in perceiving a communist hand, although not in the strong Christian organizations that form one pillar of the antinuclear movements in West Germany. Instead they perceive the communist hand in the Krefeld appeal against NATO nuclear weapons now signed by over a million West Germans.
No evidence of communist stage managing has been presented publicly, but intelligence sources point to the identical wording of part of the Krefeld appeal with earlier communist formulations - and to the wide availability of money from anonymous sources for bus and train fare to get mobile protesters from one demonstration to another in Europe.
More concretely, Denmark expelled one Soviet diplomat recently for passing money to a Danish organizer of antinuclear rallies.
West German political sources, however - including Social Democrats who have been active in antinuclear movements and have ensured that protests were directed against the existing Soviet SS-20s as well as against the planned NATO missiles - vehemently reject the thesis that the communists are anything but fringe actors in antinuclear movements here. Instead they attribute the burgeoning of grass-roots protest to widespread nuclear angst, and the breakdown of arms control talks prior to American-Soviet resumption of negotiations three weeks ago.
All of this is an old debate in Europe, however. The present lack of European resonance to Reagan's charge probably results primarily from the impact of Poland, which has tended to smother all other issues.