Ku qor sii wadida cutubkan - Guulaha ugu wanaagsan ee tartanka waxaa ka mid ah marka hore Leipzig 1975, Dubna 1976, Yerevan 1980, Banja Luka 1981, Sochi 1981 iyo Minsk 1982. Waxa uu ahaa co-guulaha tartankii 1978 ee tartanka Soviet (Mikhail Tal) iyo guusha tartanka 1986. Wuxuu ka adkaaday qaar ka mid ah horyaalkii adduunka: Vasily Smyslov ee Moscow Spartakiad 1974, Tal ee Sochi 1970, iyo Garry Kasparov oo da 'yar oo ka tirsan Horyaalka Soviet ee 1978. Tseshkovsky laftiisa ayaa ku dhowaad u qalmay tartamada musharixiinta ee Horyaalka Adduunka markii uu kaalinta afaraad ka galay 1976 Manila Interzonal, oo ka hooseysa hal boos oo looga baahnaa inuu u gudbo marxaladda xigta. Ciyaaraha Olombikada Chess-ka ee 27-aad
1986, wuxuu dhaliyay 21⁄2/5 isagoo ahaa guddiga labaad ee kaydka si uu uga caawiyo kooxda USSR inay ku guuleystaan billad dahab ah.