In the same year, 1996, Kostya wins his first title with his teammate Alexei Kharchuk - Latvian kickboxing champion (youth).

In the amateur ring, Glukhov won the world championships in Thai boxing, Kickboxing and Kick-jitsu.

In 2006 and 2008, Gluhov as part of the Latvian national team won the world championship in universal combat (unifight).

In 2007, in Sochi, Gluhov lost for WBKF world championship belt to Alexei Kudin from Belarus On November 22, 2008 Gluhov won the K-1 World Grand Prix 2008 in Riga tournament by three consecutive knockouts over Marco Della Ricca, Pacome Assi and Mindaugas Sakalauskas.

[3] March 26, 2009 in Moscow hosted a kickboxing world championship tournament, which was attended by Pavel Zhuravlev, Alexei Kudin, Konstantin Gluhov and Elvin Abbasov.