Well, during the Soviet era the Communist Party had an overt, above-ground apparatus and a covert, underground apparatus. The above-ground apparatus was the open party members--the people the CP would put up as Presidential candidates and so forth. These were linked covertly to the underground apparatus--spies, liaisons with KGB agents at the UN, liaisons with front groups and infiltrators of non-Communist organizations on the left, etc. The financial conduit supporting this was centered around Armand Hammer and some of his associates, notably Samuel Rubin whose foundation helped fund the Institute for Policy Studies, a key link between the above-ground and underground parts of the network. Rubin's daughter, Cora Weiss, shows up in connection with the Mobe and many related groups. The Mobe and New Mobe were the umbrella for a while, at least within the antiwar movement (to restrict the discussion to that, as the Communist apparatus also branches off in a lot of other directions--left-wing religious groups linked to the antiwar movement, legal groups like the ACLU and National Lawyers Guild, far-left caucuses in Congress, etc.). During the Reagan administration old elements of the New Mobe reformed under the umbrella of the Nuclear Freeze Movement. Then with the Gulf War they resurfaced among opponents of Iraq sanctions, with Ramsey Clark taking a lead role. If you look at the network of people around Ramsey Clark you find a lot of links to Vietnam-era antiwar figures. That's only scratching the surface of your question, but I hope that addresses it somewhat.
come read this
KGB Active Measures made a special project of the Nuclear Freeze and our boy John F. Kerry made it a special project of his as well.
Cora Weiss brings back old memories. My mother belonged to SANE which was run by her in the 1950s. Was a nuclear disarmament organization.