[1] In 1991 Neverov won the Capablanca Memorial in Havana,[2] and was a winner of the Politiken Cup in 1994.

[3] He took part in the FIDE World Chess Championship 2004 but was eliminated in the first round by Shakhriyar Mamedyarov.

[4] Neverov won the 2005/06 Hastings International Chess Congress.

He tied for first with Merab Gagunashvili in the 2006/07 edition of the same event, and with Nidjat Mamedov and Vadim Malakhatko in 2007/08.

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