| Tourney Name: | UEFA Cup |
| Year: | 1978–79 |
| Dates: | 5 September 1978 – 23 May 1979 |
| Champion Other: | Borussia Mönchengladbach |
| Count: | 2 |
| Second Other: | Red Star Belgrade |
| Matches: | 126 |
| Goals: | 365 |
| Attendance: | 3035950 |
| Top Scorer: | Allan Simonsen (Borussia Mönchengladbach) 9 goals |
| Prevseason: | 1977–78 |
| Nextseason: | 1979–80 |
The 1978–79 UEFA Cup was the eighth season of the UEFA Cup, the third-tier club football competition organised by UEFA. The final was played over two legs at the Red Star Stadium, Belgrade, Yugoslavia, and at the Rheinstadion, Düsseldorf, West Germany. It was won by Borussia Mönchengladbach of West Germany, who defeated Red Star Belgrade of Yugoslavia by an aggregate result of 2–1 to claim their second UEFA Cup title.
Red Star Belgrade became the third Yugoslav and second Serbian team to reach a European final, but couldn't defeat the more experienced West German side, who reached their fourth European final out of five in a seven-year span.
A total of 64 teams from 31 UEFA member associations participate in the 1978–79 UEFA Cup. The original allocation scheme was as follows:
East Germany and Bulgaria were the two associations selected to have a third birth for this season, while Poland and Switzerland went back to two qualified teams.
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The labels in the parentheses show how each team qualified for competition:
The schedule of the competition was as follows. Matches were scheduled for Wednesdays, though some matches took place on Tuesdays or Thursdays. Also, both away games for Śląsk Wrocław in the first two rounds were held on a Saturday.
| First round | 5–16 September 1978 | 14–28 September 1978 | |
| Second round | 18–21 October 1978 | 31 October – 2 November 1978 | |
| Third round | 22–23 November 1978 | 6 December 1978 | |
| Quarter-finals | 7 March 1979 | 20–21 March 1979 | |
| Semi-finals | 10–11 April 1979 | 24–25 April 1979 | |
| Final | 9 May 1979 | 23 May 1979 |
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------------------------------------Enzo Ferrero scored an olympic goal.----------------------------------------------------------------------------------------
Dukla Prague won 2–1 on aggregate.----1–1 on aggregate. Milan won in a penalty shoot-out.----Valencia won 5–3 on aggregate.----Borussia Mönchengladbach won 7–2 on aggregate.----Argeș Pitești won 5–1 on aggregate.----Ajax won 3–2 on aggregate.----Everton won 10–0 on aggregate.----Lausanne-Sport won 2–0 on aggregate.----Benfica won 2–0 on aggregate.----Sporting Gijón won 3–1 on aggregate.----Braga won 7–3 on aggregate.----West Bromwich Albion won 6–2 on aggregate.----6–6 on aggregate, Red Star Belgrade won on away goals rule.----KuPS won 6–5 on aggregate.----Stuttgart won 7–3 on aggregate.----Torpedo Moscow won 7–3 on aggregate.----Strasbourg won 4–3 on aggregate.----MSV Duisburg won 10–2 on aggregate.----Standard Liège won 1–0 on aggregate.----Esbjerg won 1–0 on aggregate.----Arsenal won 7–1 on aggregate.----Carl Zeiss Jena won 3–2 on aggregate.----1–1 on aggregate, ÍBV won on away goals rule.----Manchester City won 4–3 on aggregate.----Hibernian won 3–2 on aggregate.----Politehnica Timișoara won 3–2 on aggregate.----Śląsk Wrocław won 7–3 on aggregate.----Levski Sofia won 4–3 on aggregate.----Dinamo Tbilisi won 3–1 on aggregate.----Hajduk Split won 3–2 on aggregate.----Hertha BSC won 2–1 on aggregate.----Budapest Honvéd won 8–2 on aggregate.
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Ajax won 5–0 on aggregate.----Budapest Honvéd won 4–2 on aggregate.----2–2 on aggregate, Dukla Prague won on away goals rule.----Valencia won 6–4 on aggregate.----MSV Duisburg won 3–0 on aggregate.----Stuttgart won 3–2 on aggregate.----2–2 on aggregate, Arsenal won on away goals rule.----Hertha BSC won 2–1 on aggregate.----Śląsk Wrocław won 4–1 on aggregate.----Esbjerg won 6–1 on aggregate.----Manchester City won 4–2 on aggregate.----Milan won 4–1 on aggregate.On 23 November 1978, UEFA fined Milan $14,000 for a bribery attempt to the Scottish referee John Gordon and linesmen Rollo Kyle and David McCartney (Italian club took the officials to shop for free the day before the game). Curiously, UEFA did not sanction the referee at all, however, Scottish Football Association suspended him.----Strasbourg won 2–1 on aggregate.----West Bromwich Albion won 3–0 on aggregate.----Borussia Mönchengladbach won 2–0 on aggregate.----Red Star Belgrade won 2–1 on aggregate.
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Manchester City won 5–2 on aggregate.----Borussia Mönchengladbach won 5–3 on aggregate.----Budapest Honvéd won 4–3 on aggregate.----Hertha BSC won 5–2 on aggregate.----MSV Duisburg won 4–0 on aggregate.----Red Star Belgrade won 2–1 on aggregate.----West Bromwich Albion won 3–1 on aggregate.----Dukla Prague won 5–4 on aggregate.
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4–4 on aggregate, MSV Duisburg won on away goals rule.----Hertha BSC won 3–2 on aggregate.----Borussia Mönchengladbach won 4–2 on aggregate.----Red Star Belgrade won 2–1 on aggregate.
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Borussia Mönchengladbach won 6–3 on aggregate.----2–2 on aggregate, Red Star Belgrade won on away goals rule.
See main article: 1979 UEFA Cup Final.
Borussia Mönchengladbach won 2–1 on aggregate.