The 1984/85 UEFA Cup was the 14th edition of the competition organized by UEFA . In the finals, the Spanish representative Real Madrid prevailed after two finals against the Hungarian representative Videoton SC and won the cup for the first time.
Albanian associations did not take part for political reasons. Ajax Amsterdam won the second leg of the first round against the Luxembourg club Red Boys Differdange with 14: 0, the highest win without conceding in European cup history. The Partizan Belgrade team succeeded in the second round as the first team in the history of the UEFA Cup and as the second team in the European Cup at all (after the Leixões SC , which won this success in the first round of the 1961/62 European Cup Winners' Cup succeeded) to make up a 4-goal deficit from the first leg and advance to the next round.
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The competition was played in six rounds in two legs. In the event of a tie, the number of goals scored away decided first, followed by extra time and finally the penalty shoot-out.