| Tourney Name: | UEFA Cup |
| Year: | 1984–85 |
| Dates: | 18 September 1984 - 22 May 1985 |
| Champion Other: | Real Madrid |
| Count: | 1 |
| Second Other: | Videoton |
| Matches: | 126 |
| Goals: | 356 |
| Top Scorer: | József Szabó (Videoton) 8 goals |
| Prevseason: | 1983–84 |
| Nextseason: | 1985–86 |
The 1984–85 UEFA Cup was the 14th season of the UEFA Cup, the third-tier club football competition organised by the Union of European Football Associations (UEFA). The final was played over two legs at the Sóstói Stadion, Székesfehérvár, Hungary, and at the Santiago Bernabéu Stadium, Madrid, Spain. The competition was won by Real Madrid of Spain, who defeated Videoton of Hungary by an aggregate result of 3–1 to claim their first UEFA Cup title.
Real Madrid became the first Spanish side to win the UEFA Cup since its foundation in 1971. Three Spanish teams had won the predecessor tournament, the Inter-Cities Fairs' Cup, but UEFA does not recognise it as an official competition within its records. The last Spanish title at this level was achieved 18 years before, by long-time rivals Barcelona in 1966.
A total of 64 teams from 31 UEFA member associations participated in the 1984–85 UEFA Cup, all entering from the first round over six knock-out rounds. The association ranking based on the UEFA country coefficients is used to determine the number of participating teams for each association:
For the 1984–85 UEFA Cup, the associations are allocated places according to their 1983 UEFA country coefficients, which takes into account their performance in European competitions from 1978–79 to 1982–83.
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The labels in parentheses show how each team qualified for competition:
The schedule of the competition was as follows. Matches were scheduled for Wednesdays, though some matches exceptionally took place on Tuesdays or Thursdays.
| First round | 12–20 September 1984 | 2–3 October 1984 | |
| Second round | 24 October 1984 | 7–8 November 1984 | |
| Third round | 28 November 1984 | 12 December 1984 | |
| Quarter-finals | 6 March 1985 | 20 March 1985 | |
| Semi-finals | 10 April 1985 | 24 April 1985 | |
| Final | 8 May 1985 | 22 May 1985 |
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Videoton won 1–0 on aggregate.----Queens Park Rangers won 7–0 on aggregate.----1–1 on aggregate; Universitatea Craiova won 5–3 on penalties.----Lokomotive Leipzig won 7–3 on aggregate.----Köln won 3–1 on aggregate.----Željezničar won 5–2 on aggregate.----Spartak Moskva won 7–2 on aggregate.----Dinamo Minsk won 10–0 on aggregate.----Partizan won 4–0 on aggregate.----Rijeka won 4–2 on aggregate.----CSKA Septemvriysko Zname won 4–3 on aggregate.----Bohemians ČKD Praha won 8–3 on aggregate.----Manchester United won 5–2 on aggregate.----PSV Eindhoven won 3–2 on aggregate.----Widzew Łódź won 2–1 on aggregate.----Fiorentina won 3–0 on aggregate.----Borussia Mönchengladbach won 7–3 on aggregate.----Standard Liège won 3–1 on aggregate.----Club Brugge won 1–0 on aggregate.----Olympiacos won 3–2 on aggregate.----Linzer ASK won 2–0 on aggregate.----Real Madrid won 5–2 on aggregate.----Hamburg won 2–0 on aggregate.----Sporting CP won 4–2 on aggregate.----Ajax won 14–0 on aggregate.----Dundee United won 3–1 on aggregate.----Rangers won 4–3 on aggregate.----Paris Saint-Germain won 6–2 on aggregate.----2–2 on aggregate; Anderlecht won on away goals.----Internazionale won 2–1 on aggregate.----Sion won 4–2 on aggregate.----Tottenham Hotspur won 9–0 on aggregate.
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Spartak Moskva won 3–1 on aggregate.----2–2 on aggregate; Dinamo Minsk won 5–3 on penalties.----1–1 on aggregate; Bohemians ČKD Praha won 4–2 on penalties.----3–3 on aggregate; Widzew Łódź won on away goals.----Hamburg won 6–1 on aggregate.----6–6 on aggregate; Partizan won on away goals.----Universitatea Craiova won 2–0 on aggregate.----Anderlecht won 7–3 on aggregate.----Željezničar won 3–2 on aggregate.----Köln won 4–1 on aggregate.----Internazionale won 4–3 on aggregate.----Dundee United won 7–2 on aggregate.----Manchester United won 1–0 on aggregate.----Tottenham Hotspur won 4–2 on aggregate.----Real Madrid won 4–3 on aggregate.----Videoton won 5–2 on aggregate.
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Željezničar won 4–2 on aggregate.----Tottenham Hotspur won 3–1 on aggregate.----Videoton won 5–2 on aggregate.----Dinamo Minsk won 2–1 on aggregate.----Köln won 2–1 on aggregate.----2–2 on aggregate; Internazionale won on away goals.----Manchester United won 5–4 on aggregate.----Real Madrid won 6–4 on aggregate.
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1–1 on aggregate; Videoton won 5–4 on penalties.----Željezničar won 3–1 on aggregate.----Internazionale won 4–1 on aggregate.----Real Madrid won 1–0 on aggregate.
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Videoton won 4–3 on aggregate.----Real Madrid won 3–2 on aggregate.
See main article: 1985 UEFA Cup Final.
Real Madrid won 3–1 on aggregate.