Živojinović was multiple Yugoslav youth champion. He won the junior title of the Italian Open in 1981 and became a professional tennis player that same year. In 1984 he reached his first quarter-finals on the ATP World Tour in Kitzbühel . The following year he was in the final of the ATP tournament in Nancy and the Challenger tournament in Thessaloniki . He was also in the semi-finals of the Queen's Club Championships and won his first ATP double title at the side of Libor Pimek in Boston . In 1986 he finally won his first of two singles titles, and in the course of his career he also won eight tournaments in doubles. He achieved his best scores in the world rankings in 1987 with position 19 in singles and 1986 with first place in doubles.
Živojinović played 39 singles and 23 doubles games for the Yugoslav Davis Cup team between 1981 and 1992 . His greatest successes with the team were the semi-finals in the world group in 1988 and 1991. In the 5-0 defeat in the semi-finals against Germany , he lost against Boris Becker and Eric Jelen both singles and the doubles game on the side of Goran Ivanišević . Even in the 5-0 semi-final defeat against France , he was unable to win his singles or doubles game. In 1988 he competed in the Olympic Games for Yugoslavia in singles and doubles. In the singles he failed in round two to Guy Forget , with his doubles partner Goran Ivanišević he advanced to the quarter-finals, in which they were defeated by the later silver medalists Sergio Casal and Emilio Sánchez Vicario from Spain.
Živojinović has been married to the singer Lepa Brena for the second time since 1991 . In addition to a son from his first marriage, Živojinović has two other sons with Brena. In November 2000, their eight-year-old son Stefan was kidnapped and released five days later after paying a ransom . The police caught the perpetrators in 2003 as part of the Sablja police operation .
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Yugoslavia
Houston
Sydney
Libor Pimek
Boris Becker
Rotterdam
Stefan Edberg
Wojciech Fibak Matt Mitchell
Andrés Gómez
Milan
Sergio Casal Emilio Sánchez Vicario
Tokyo
