Mezue ahịrịokwu na-esonụ: N'afọ 1991, Neverov meriri Ememe Ncheta Capablanca na Havana, ma bụrụ onye mmeri nke Politiken Cup na 1994. Ọ gbaara mba Ukraine bọọlụ na
35th Chess Olympiad na Bled 2002. O sonyere na FIDE World Chess Championship 2004 mana Shakhriyar Mamedyarov kpochapụrụ ya na agba nke mbụ. Neverov meriri na 2005/06 Hastings International Chess Congress. Ya na Merab Gagunashvili jikọrọ nke mbụ na mbipụta 2006/07 nke otu ihe omume ahụ, yana Nidjat Mamedov na Vadim Malakhatko na 2007/08.