The Counterculture Movement was American, but other nations had their own counterculture movements, with the Stilyagi being the one I'm most aware of.

Yes, the Counterculture Movement in the United States coincided with, and helped to spawn, other movements in Europe. Historians typically view the height of these movements to be 1968--the year of the Martin Luther King assassination riots and the anti-war Democratic Convention riots in the United States; the year that strikes shut down France and force De Gaulle to flee the nation; the year that the Prague Spring in Czechoslovakia challenged the status quo in Eastern Europe by offering a new take on socialism, which compelled the Soviet Union to invade--and you'll find that research on the links between the American and European upheavals generally center on that year. Jiri (Jeremy) Suri analyzes these links in his The Global Revolutions of 1968 (2007) which is not printed on an academic press, but his Power and Protest: Global Revolution and the Rise of Detente (2005), which looks at the role of these protests in the formation of international policy in the United States, China, and the Soviet Union, is on the Harvard University Press (he's an expert on the topic of protest). There are other books that cover the upheaval of 1968 if you are interested.

But it was not just protests that defined the Counterculture Movement. Counterculture itself also helped to define this movement. And you certainly see counterculture rise in European nations in tandem with the United States (I am stepping outside my area of research here, except in relation to Czechoslovakia). In Czechoslovakia, for example, a "Czech New Wave" in film challenged Communist-sanctioned film through experimentation and anti-government themes. Some of these movies embrace Western surrealism and absurdism, such as Daises (1966) (I cant fully make sense of this movie), while other films challenged effectiveness of the Communist Party, such as Closely Watched Trains (1967) and The Joke (1968). Closely Watched Trains has excellent English subtitles and acts as a great introduction to Czech film, I think (note that it takes place during the German occupation of Czechoslovakia in the 1940s as a means to critique Soviet domination of Czechoslovakia in the 1960s). These movies were often adaptations of novels which themselves represented counterculture. Similarly, the band Plastic People of the Universe (formed in 1968) embraced American and British experimental music as a form of protest against the status quo. And here it is not ambiguous: they sang in English because English was the language of rock music. The Czechoslovak government arrested the band in 1977, which helped to set off the "Charter 77" movement that eventually seized control of the Czechoslovak government when the Soviet empire crumbled.

/u/scalfin has argued that "other nations had their own counterculture movements" as though there were no links between the American Counterculture movement and similar movements abroad that occurred at the same time and often with equal (and sometimes greater) intensity. I would suggest looking at Suri's book before coming to that conclusion. Unfortunately, I have not annotated the book, and so I cannot provide you with as good of an answer as I'd like. I'd also warn you that the Soviet movement he mentioned corresponded more with Beatnik culture than the counterculture of the 1960s & 1970s, and that Russia did experience its own internationally-inspired protests in 1968.