 Pari gbolohun ti o tẹle: Ni ipele ọdọ, Alibegović dun fun awọn ẹgbẹ orilẹ-ede Yugoslavia labẹ 18 ati labẹ 19, eyiti o gba 1986 FIBA European Under-18 Championship, ati 1987 FIBA Under-19 World Cup. Alibegović je omo egbe agbaboolu agbaboolu orile-ede Slovenia, lati 1991 si 2001. Pẹlu Slovenia, o ṣe ere ni EuroBaskets mẹrin 1993, 1995, : 1997, 2001. Pẹlu ẹgbẹ agbabọọlu agbalagba orilẹ-ede Slovenia, o dun ni awọn ere 52, o si gba awọn aaye 990, eyiti o jẹ ki o jẹ oludije ti o ga julọ ni gbogbo igba ti ẹgbẹ agbabọọlu bọọlu afẹsẹgba agbalagba ti Slovenia. 