Pedzisa mutsara unotevera: Muna 1991 Neverov akakunda Capablanca Chirangaridzo muHavana, uye akanga ari mukundi wePolitiken Cup muna 1994. Akatambira Ukraine mu
35th Chess Olympiad paBled 2002. Akatora chikamu muFIDE World Chess Championship 2004 asi akabviswa mumutambo wokutanga naShakhriyar Mamedyarov. Neverov akakunda Hastings International Chess Congress muna 2005/06. Akafananidza wekutanga naMerab Gagunashvili muna 2006/07 edition yechiitiko chimwe chete, uye naNidjat Mamedov naVadim Malakhatko muna 2007/08.