| 1. Round | 14/09/1977 | BK Frem København | - | Grasshopper Club Zürich | 0:2 | ||||
| 1. Round | 28/09/1977 | Grasshopper Club Zürich | - | BK Frem København | 6:1 |  |
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| 2. Round | 19/10/1977 | TJ Internacionál Slovnaft Bratislava | - | Grasshopper Club Zürich | 1:0 | ||||
| 2. Round | 01/11/1977 | Grasshopper Club Zürich | - | TJ Internacionál Slovnaft Bratislava | 5:1 | |
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| Round of 16 | 22/11/1977 | Dinamo Tbilisi | - | Grasshopper Club Zürich | 1:0 | ||||
| Round of 16 | 06/12/1977 | Grasshopper Club Zürich | - | Dinamo Tbilisi | 4:0 | |
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| Quarter-finals | 28/02/1978 | Eintracht Frankfurt | - | Grasshopper Club Zürich | 3:2 | |
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| Quarter-finals | 13/03/1978 | Grasshopper Club Zürich | - | Eintracht Frankfurt | 1:0 | |
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| Semi-finals | 29/03/1978 | Grasshopper Club Zürich | - | SC Bastia | 3:2 | |
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| Semi-finals | 12/04/1978 | SC Bastia | - | Grasshopper Club Zürich | 1:0 |
Italy