Late in World War II, a number of green US pilots engaged allied (usually Soviet) fighters on accident. Ivan Kozhedub, the top Soviet ace, supposedly was jumped in his Lavochkin La-7 by two American pilots flying North American P-51 Mustangs. Being who he was, he shot both down. Story is unconfirmed and possibly apocryphal.

During the Korean War, the cream of the Communist pilots were Soviet pilots who were there in an unofficial capacity. as were some ground forces like this anti-aircraft division. The pilots had to sign nondisclosure agreements. They were based in China near the Yalu River border with North Korea, and forbidden from flying within 30-50 miles of UN controlled territory. One pilot committed suicide when he was shot down near UN lines and another was strafed by his own men. F-86 pilots were not allowed to attack airfields in China but frequently broke rules of engagement and did so. A few pilots even reported visual sighting of Mig-15 pilots, one of whom had "red hair and big bushy eyebrows" and did not look Korean or Chinese at all. Soviet involvement in Korea, beyond Stalin prodding Kim Il-Sung, was widely suspected but not confirmed until reports came out during Glasnost and the collapse of the Soviet Union.

Felgenhauer, Pavel. "Russia's Secret Operations." Perspective XII, no. 1 (September-October 2001).

Кожедуб И. Н. Верность Отчизне. Ищущий боя. — М.: Эксмо, 2006. ISBN 5-699-17415-X, page 9.

Lashmar, Paul. "Stalin's Hot War." New Statesman and Society 9, no. 388, (February 2, 1996).

Zaloga, Steven J. "The Russians in MiG Alley: The nationality of the "honcho" pilots is no longer a mystery. The Soviets now admit their part in the Korean War" Air Force Magazine, volume 74, issue 2, February 1991.

The Polar Bear Expedition during the Russian Civil War was part of the Allies' intervention in the Russian Civil War after the end of WW1. In this expedition several thousand U.S. soldiers fought Red Army troops around Arkhangelsk for several months.

edit: books on the topic:

Bozich, Stanley J. and Jon R. Bozich (1985). "Detroit's Own" Polar Bears: The American North Russian Expeditionary Forces 1918-1919.

Gordon, Dennis (1982). Quartered In Hell: The Story of American North Russian Expeditionary Force 1918-1919

Hendrick, Michael (1972). An Investigation of American Siberian intervention (1918-1920)

Jahns, Lewis E., The History of the American Expedition Fighting the Bolsheviki Campaigning in North Russia 1918-1919