[2] In 2006 Alekseev won the Russian Championship Superfinal after defeating Dmitry Jakovenko in a playoff match.

[3] By winning the 2007 Aeroflot Open in Moscow,[4] Alekseev qualified for the 2007 Dortmund Sparkassen Chess Meeting.

In this latter event he shared the second place – behind World Champion Vladimir Kramnik – with Viswanathan Anand and Péter Lékó.

In 2008 Alekseev won the 41st Biel Chess Festival after a playoff with Leinier Domínguez.

[8] In the European Individual Chess Championship of 2013, he tied for first place with nine other players points and took the silver medal on tiebreak.