At international level, Živković represented the Croatia national team making 39 appearances, 18 of which as the captain of the team.
Club career
Early career
Živković started his career at Sarajevo as a youth player, before being signed by Marsonia (from Slavonski Brod). He gained a good reputation at Marsonia, first appearing in the 1994–95 season, during which he made 13 appearances. The next season, he played a further 31 games before transferring to Hrvatski Dragovoljac (from Siget, Zagreb). He only spent one season at his new club however, before impressive performances persuaded German club Bayer Leverkusen to sign him.
Bayer Leverkusen
Živković went on to play six seasons for the German club, playing over 150 times, including the 2002 UEFA Champions League Final. Following his contract expiring in the summer of 2003, Živković stated his desire to play in the Premier League, and was signed later that summer by Portsmouth.
Portsmouth and Stuttgart
Živković started his Pompey career well, instantly claiming a regular starting place. However, in December, a public fall-out with manager Harry Redknapp led to him being released, having played only 18 times for the club. VfB Stuttgart stepped in to bring Živković back to Germany, and the Croatian joined them in January.
Živković was a regular for the Croatia national team, making 39 appearances and scoring twice.[3] He was part of the squad at the 2002 FIFA World Cup, but in his first game against Mexico, he caused a penalty in the 59th minute after which he was sent off and the Mexicans went on to score from the penalty mark and win the game by 1-0. He was no longer in the team for the remaining two games Croatia played on the tournament before being eliminated — Italy and Mexico progressed from the group to the playoffs instead.