Kammala jumla mai zuwa: A cikin 1991 Neverov ya lashe Gidan Tunawa da Capablanca a Havana, kuma ya lashe gasar Politiken a 1994. Ya buga wa Ukraine wasa a gasar
Gasar Olympics ta Chess ta 35 a Bled 2002. Ya halarci Gasar Cin Kofin Duniya ta FIDE ta 2004 amma Shakhriyar Mamedyarov ya fitar da shi a zagaye na farko. Neverov ya lashe gasar wasan Chess ta kasa da kasa ta Hastings a shekarar 2005/06. Ya yi daidai da na farko tare da Merab Gagunashvili a shekarar 2006/07 na wannan taron, da Nidjat Mamedov da Vadim Malakhatko a 2007/08.