Kammala jumla mai zuwa: Balashov ya wakilci USSR a cikin ƙungiyoyi da yawa. Ya buga wasa a tebur na biyu don ƙungiyar USSR a 1971, 1972, da 1974 Gasar Teamungiyar Studentungiyar Studentasa ta Duniya, inda ya sami lambar zinare ta biyu a 1971, lokacin da ya zama babban mashahurin ƙasa da ƙasa, tare da maki 61⁄2/8 maki. Balashov ya taka leda a gasar zakarun Turai guda hudu, 1970, 1973, 1977, da 1980, inda ya lashe lambar zinare a kan tebur na biyar a 1977. A cikin
24th Chess Olympiad a 1980, ya ci 71⁄2/10 a matsayin ajiyar jirgi na farko don taimakawa ƙungiyar USSR ta lashe lambar zinare.