| 2. Round | 08/03/1998 | Grasshopper Club Zürich | - | FC Aarau | 5:3 |  |
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| 3. Round | 15/03/1998 | FC Zürich | - | Grasshopper Club Zürich | 0:2 | |
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| 4. Round | 21/03/1998 | Grasshopper Club Zürich | - | FC St. Gallen | 2:2 | |
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| 5. Round | 29/03/1998 | Lausanne Sports | - | Grasshopper Club Zürich | 2:1 | |
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| 6. Round | 05/04/1998 | Grasshopper Club Zürich | - | FC Sion | 5:2 | ||||
| 7. Round | 11/04/1998 | FC Luzern | - | Grasshopper Club Zürich | 0:3 | |
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| 9. Round | 25/04/1998 | FC Sion | - | Grasshopper Club Zürich | 1:2 | |
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| 10. Round | 28/04/1998 | Grasshopper Club Zürich | - | Lausanne Sports | 3:0 | |
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| 11. Round | 02/05/1998 | FC St. Gallen | - | Grasshopper Club Zürich | 1:2 | |
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| 12. Round | 08/05/1998 | Grasshopper Club Zürich | - | FC Zürich | 2:1 |
Argentina