| 1. Round | 28/09/1977 | Grasshopper Club Zürich | - | BK Frem København | 6:1 | ||||
| 2. Round | 19/10/1977 | TJ Internacionál Slovnaft Bratislava | - | Grasshopper Club Zürich | 1:0 | ||||
| Quarter-finals | 28/02/1978 | Eintracht Frankfurt | - | Grasshopper Club Zürich | 3:2 | ||||
| Quarter-finals | 13/03/1978 | Grasshopper Club Zürich | - | Eintracht Frankfurt | 1:0 | ||||
| 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 |
Switzerland