In 1993 he settled in Slovakia, and from the following year Gennadij Timoscenko represented this country in the international chess tournaments.
Gennadij Timoscenko has achieved many successes in international chess tournaments, winning or sharing first place among others in Rimavská Sobota (1974), Polanica-Zdrój (1976, Rubinstein Memorial),[6] Varna (1977), Słupsk (1979), Helsinki (1986, together with Jón Loftur Árnason), London (1992, together with Jon Speelman), Šaľa (1994), Starý Smokovec (1996), Bolzano (1998), Seefeld (1998, 1999), Padua (1998, 2000 from Erald Dervishi), Cutro (2000), Graz (2003) and in Opatija (2003).
In 2010 and 2011 he won bronze medals twice in a row in the European Senior Chess Championship in the S60 age group (players over 60 years old).
In 2011, in Opatija he also won the bronze medal in the World Senior Chess Championship in the same age category.
Gennadij Timoscenko played for Slovakia in the Chess Olympiads:[7] Gennadij Timoscenko played for Slovakia in the European Team Chess Championship:[8] In 1976, he was awarded the FIDE International Master (IM) title and received the FIDE Grandmaster (GM) title in 1980.