| First Qualifying Round | 16/09/1978 | Yeovil Town | 4 - 0 | Andover | 1,196 |
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| Second Qualifying Round | 07/10/1978 | Hungerford Town | 4 - 4 | Yeovil Town | |
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| Second Qualifying Round Replay | 11/10/1978 | Yeovil Town | 3 - 0 | Hungerford Town | |
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| Third Qualifying Round | 21/10/1978 | Yeovil Town | 2 - 1 | Dorchester Town | 1,935 |
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| Fourth Qualifying Round | 04/11/1978 | Cheltenham Town | 1 - 2 | Yeovil Town | 1,783 |
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| Round One | 25/11/1978 | Yeovil Town | 0 - 1 | Barking | 3,070 |
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| Round Three | 04/04/1979 | Yeovil Town | 1 - 0 | Frome Town | |
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| Semi Final | 18/04/1979 | Yeovil Town | 4 - 2 | Bath City | |
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| Final First Leg | 15/05/1979 | Minehead | 1 - 1 | Yeovil Town | |
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| Final Second Leg | 17/05/1979 | Yeovil Town | 3 - 2 | Minehead | |
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| Third Qualifying Round | 02/12/1978 | Yeovil Town | 8 - 1 | Merthyr Tydfil | 1,497 |
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| Round One | 13/01/1979 | Yeovil Town | 3 - 0 | Falmouth Town | 1,235 |
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| Round Two | 03/02/1979 | Yeovil Town | 5 - 0 | Barrow | 2,237 |
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| Round Three | 24/02/1979 | Leatherhead | 0 - 1 | Yeovil Town | 1,800 |
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| Round Four | 17/03/1979 | Dagenham | 2 - 0 | Yeovil Town | 1,792 |
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| Round One Leg One | 19/08/1978 | Yeovil Town | 2 - 0 | Trowbridge Town | |
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| Round One Leg Two | 22/08/1978 | Trowbridge Town | 2 - 0 | Yeovil Town | |
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| Round One Replay | 05/09/1978 | Trowbridge Town | 1 - 2 | Yeovil Town | |
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| Round Two | 26/09/1978 | Dorchester Town | 0 - 0 | Yeovil Town | |
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| Round Two Replay | 25/10/1978 | Yeovil Town | 3 - 0 | Dorchester Town | |
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| Round Three | 15/11/1978 | Yeovil Town | 2 - 0 | Barry Town | |
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| Round Four | 19/02/1979 | Worcester City | 2 - 2 | Yeovil Town | |
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| Round Four Replay | 26/02/1979 | Yeovil Town | 4 - 1 | Worcester City | |
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| Semi Final Leg One | 07/03/1979 | Weymouth | 1 - 1 | Yeovil Town | |
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| Semi Final Leg Two | 19/03/1979 | Yeovil Town | 1 - 0 | Weymouth | |
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| Final First Leg | 07/04/1979 | Bath City | 1 - 0 | Yeovil Town | |
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| Final Second Leg | 14/04/1979 | Yeovil Town | 0 - 0 | Bath City | |
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Western Counties Floodlight Cup
| 06/12/1978 | Yeovil Town | 5 - 0 | Salisbury | |
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| 26/03/1979 | Poole Town | 3 - 0 | Yeovil Town | |
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| 22/04/1979 | Dorchester Town | 1 - 0 | Yeovil Town | |
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| 26/04/1979 | Yeovil Town | 1 - 3 | Weymouth | |
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