| 9. Round | 04/11/1978 | Hércules CF | - | Athletic Club | 0:1 | ||||
| 11. Round | 25/11/1978 | Hércules CF | - | Burgos CF | 1:0 | ||||
| 25. Round | 25/03/1979 | Hércules CF | - | Real Sociedad | 0:0 | ||||
| 28. Round | 22/04/1979 | Burgos CF | - | Hércules CF | 0:0 | ||||
| 29. Round | 29/04/1979 | Hércules CF | - | Sevilla FC | 1:0 |
Spain