1977-78 Scottish Cup
| Final | ||||||
| Rangers | 2 | 1 | Aberdeen | Sat 06 May 1978 | Details | |
| Semi Final | ||||||
| Rangers | 2 | 0 | Dundee United | Wed 05 Apr 1978 | Details | |
| Aberdeen | 4 | 2 | Partick Thistle | Wed 12 Apr 1978 | Details | |
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| 5th Round | ||||||
| Dundee United | 2 | 0 | Queen's Park | Sat 11 Mar 1978 | Details | |
| Partick Thistle | 2 | 1 | Dumbarton | Sat 11 Mar 1978 | Details | |
| Aberdeen | 2 | 2 | Greenock Morton | Sat 11 Mar 1978 | Details | |
| Rangers | 4 | 1 | Kilmarnock | Sat 11 Mar 1978 | Details | |
| Greenock Morton | 1 | 2 | Aberdeen | Wed 15 Mar 1978 | 1st Replay | Details |
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| 4th Round | ||||||
| Rangers | 1 | 0 | Stirling Albion | Sat 18 Feb 1978 | Details | |
| Greenock Morton | 3 | 0 | Meadowbank Thistle | Sat 18 Feb 1978 | Details | |
| Dumbarton | 1 | 1 | Hearts | Sat 18 Feb 1978 | Details | |
| Aberdeen | 3 | 0 | St Johnstone | Mon 27 Feb 1978 | Details | |
| Hearts | 0 | 1 | Dumbarton | Mon 27 Feb 1978 | 1st Replay | Details |
| Motherwell | 1 | 3 | Queen's Park | Mon 27 Feb 1978 | Details | |
| Dundee United | 3 | 0 | Queen Of The South | Mon 27 Feb 1978 | Details | |
| Celtic | 1 | 1 | Kilmarnock | Mon 27 Feb 1978 | Details | |
| Hibernian | 0 | 0 | Partick Thistle | Sat 04 Mar 1978 | Details | |
| Kilmarnock | 1 | 0 | Celtic | Mon 06 Mar 1978 | 1st Replay | Details |
| Partick Thistle | 2 | 1 | Hibernian | Tue 07 Mar 1978 | 1st Replay | Details |
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| 3rd Round | ||||||
| Hamilton | 1 | 4 | Dundee United | Sat 28 Jan 1978 | Details | |
| Arbroath | 0 | 4 | Motherwell | Sat 28 Jan 1978 | Details | |
| Berwick Rangers | 2 | 4 | Rangers | Sat 28 Jan 1978 | Details | |
| Queen Of The South | 2 | 2 | Montrose | Sat 28 Jan 1978 | Details | |
| Meadowbank Thistle | 2 | 1 | Caledonian | Sat 28 Jan 1978 | Details | |
| Hibernian | 4 | 0 | East Fife | Sat 28 Jan 1978 | Details | |
| Alloa Athletic | 2 | 2 | Dumbarton | Sun 29 Jan 1978 | Details | |
| Vale Of Leithen | 0 | 1 | Queen's Park | Sat 04 Feb 1978 | Details | |
| Albion Rovers | 0 | 1 | Greenock Morton | Sun 05 Feb 1978 | Details | |
| Partick Thistle | 1 | 1 | Cowdenbeath | Sun 05 Feb 1978 | Details | |
| Montrose | 1 | 3 | Queen Of The South | Mon 06 Feb 1978 | 1st Replay | Details |
| Dumbarton | 2 | 1 | Alloa Athletic | Mon 06 Feb 1978 | 1st Replay | Details |
| Aberdeen | 2 | 0 | Ayr United | Mon 06 Feb 1978 | Details | |
| Airdrieonians | 2 | 3 | Hearts | Mon 06 Feb 1978 | Details | |
| Celtic | 7 | 1 | Dundee | Mon 06 Feb 1978 | Details | |
| St Mirren | 1 | 2 | Kilmarnock | Mon 06 Feb 1978 | Details | |
| Stirling Albion | 3 | 0 | Clydebank | Tue 07 Feb 1978 | Details | |
| St Johnstone | 1 | 0 | Brechin City | Tue 07 Feb 1978 | Details | |
| Cowdenbeath | 0 | 1 | Partick Thistle | Mon 27 Feb 1978 | 1st Replay | Details |
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| 2nd Round | ||||||
| Stranraer | 0 | 1 | Queen's Park | Sat 07 Jan 1978 | Details | |
| Vale Of Leithen | 4 | 1 | Forfar Athletic | Sat 07 Jan 1978 | Details | |
| Meadowbank Thistle | 2 | 1 | East Stirlingshire | Sat 07 Jan 1978 | Details | |
| Albion Rovers | 1 | 0 | Buckie Thistle | Sat 07 Jan 1978 | Details | |
| Berwick Rangers | 6 | 0 | Raith Rovers | Sat 07 Jan 1978 | Details | |
| Caledonian | 4 | 0 | Civil Service Strollers | Sat 07 Jan 1978 | Details | |
| Brechin City | 1 | 0 | Dunfermline Athletic | Sat 07 Jan 1978 | Details | |
| Peterhead | 1 | 1 | Cowdenbeath | Sat 07 Jan 1978 | Details | |
| Cowdenbeath | 5 | 0 | Peterhead | Sat 14 Jan 1978 | 1st Replay | Details |
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| 1st Round | ||||||
| Brechin City | 2 | 0 | Falkirk | Sat 17 Dec 1977 | Details | |
| Burntisland Shipyard | 1 | 4 | Berwick Rangers | Sat 17 Dec 1977 | Details | |
| Clyde | 0 | 3 | Dunfermline Athletic | Wed 21 Dec 1977 | 1st Replay | Details |
| Civil Service Strollers | 4 | 3 | Selkirk | Sat 07 Jan 1978 | Details | |
| Caledonian | 5 | 0 | Inverness Thistle | Sat 07 Jan 1978 | Details | |
| Raith Rovers | 1 | 0 | Stenhousemuir | Sat 07 Jan 1978 | Details | |
| Dunfermline Athletic | 0 | 0 | Clyde | Sat 07 Jan 1978 | Details | |
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