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He made first European appearance in a Basel shirt on August 13, 2008 as a substitute in a 0–0 Champions League Qualifying match draw against Vitória S.C. at Estádio D. Afonso Henriques.
Bebek is considered the best Croatian referee and is the only Croatian referee who supervised two UEFA Champions League group stage matches (Lazio v. Werder Bremen during the 2007–08 season and Bordeaux v. CFR Cluj in the 2008–09 season).