| 5. Round | 03/09/1977 | BSC Young Boys | - | Grasshopper Club Zürich | 1:4 |  |
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| 6. Round | 17/09/1977 | Grasshopper Club Zürich | - | CS Chênois | 5:1 | ||||
| 9. Round | 08/10/1977 | Neuchâtel Xamax FC | - | Grasshopper Club Zürich | 2:3 | ||||
| 11. Round | 22/10/1977 | Servette FC | - | Grasshopper Club Zürich | 2:2 | ||||
| 15. Round | 19/11/1977 | Grasshopper Club Zürich | - | BSC Young Boys | 3:0 | ||||
| 20. Round | 05/03/1978 | FC Zürich | - | Grasshopper Club Zürich | 1:2 | ||||
| 19. Round | 11/03/1978 | Grasshopper Club Zürich | - | Neuchâtel Xamax FC | 2:0 | |
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| 21. Round | 19/03/1978 | Grasshopper Club Zürich | - | Servette FC | 0:1 | ||||
| 22. Round | 22/03/1978 | FC Basel 1893 | - | Grasshopper Club Zürich | 2:5 |
Switzerland