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Slavnic's biggest successes were achieved in a Red Star Belgrade jersey, as during the 1967–1977 period, he won two Yugoslavia League championships, three Yugoslavian Cups, and the FIBA European Cup Winner's Cup (later renamed FIBA Saporta Cup). Together with Dragan Kapičić, Duci Simonović, and Vladimir Cvetković, he was a member of one of greatest team in Red Star's history. While playing for Joventut, he helped the Spanish side to win the country's Spanish League championship in 1978, for the second time in the club's history. After that, he came back to Yugoslav basketball, playing for Sibenka, and after that, he played with Caserta in the Italian 2nd Division. He finished his playing career in that club, but after a short period in Red Star's biggest rivals, Partizan Belgrade. Together with legendary Yugoslav head coach, professor Aca Nikolić, he's the only person who both played and coached, Red Star and Partizan.
Unanimously, the executive board of the Serbian Basketball Federation, decided on 29 May 2007, that Slavnić should be the head coach of the first senior national team of Serbia; after the state union with Montenegro had ceased to exist. After numerous "thanks, but no thanks" decisions of experienced players, who didn't want to participate at EuroBasket 2007, Slavnić selected Milan Gurović, Marko Jarić, Darko Miličić, and nine debutantes, who later became standard members of the senior Serbian national team. But, due to defeats to Russia, who went on to take the title, then Greece, who were the defending European champions, and won in overtime, and Israel, Serbia were eliminated in the first phase of the continental championship. The Serbian Basketball Federation decided on 26 September 2007, to look for a new head coach.
Miscellaneous
Together with his dribbling, Zoran Slavnić had three moves that were highlights of his career:
1975 - He scored over his own head against Spain, at the 1975 EuroBasket, in Belgrade,
1976 - He scored one second before the end of regulation against Italy, and won the game that sent Yugoslavia to the semifinals of the 1976 Summer Olympic Games, in Montreal.
The Spaniards called him, "The Eccentric Genius", due to his original style of play. His personal motto during his playing days was, "This is all just a game."
2007 - Serbian authorities announced that Slavnić was among those who would receive "national sports recognition for his contribution to the development and affirmation of sport."