OK. The only communist "world power" at the time was USSR (Soviet Union) that was factually dominated and controlled by Russia. They had from the very beginning (revolution in Russia) dreamed about the world domination. They tried already right after the revolution to overtake Europe but were stopped by Poland. Next attempt was during WW2 but they were first stopped by Germany and then by US (partially, as even part of Germany was occupied by them).

USSR had very wide spy network and they had considerably infiltrated US.

China was also overtaken by communists and had some influence among some naive Western intellectuals but I don't know about direct influence in US (maybe it existed, I'm just not aware of it).

These days of course both Russia and China are actively attempting to extend their influence through spy networks or by manipulations in social media (and yes, there are also obvious shill accounts here).