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| 1st(1st leg) | KB København | - | FC Schalke 04 | 3:0 (2:0) | ||
| 2nd (2nd leg) | FC Schalke 04 | - | KB København | 5:2 (2:0) | ||
| 1st(1st leg): 26/08/1958 | 2nd (2nd leg): 17/09/1958 | Winner: KB København | ||||
| 1st(1st leg) | Standard Liège | - | Heart of Midlothian | 5:1 (2:1) | ||
| 2nd (2nd leg) | Heart of Midlothian | - | Standard Liège | 2:1 (0:0) | ||
| 1st(1st leg): 03/09/1958 | 2nd (2nd leg): 09/09/1958 | Winner: Standard Liège | ||||
| 1st(1st leg) | Dinamo Zagreb | - | AS Dukla Praha | 2:2 (0:1) | ||
| 2nd (2nd leg) | AS Dukla Praha | - | Dinamo Zagreb | 2:1 (1:1) | ||
| 1st(1st leg): 10/09/1958 | 2nd (2nd leg): 01/10/1958 | Winner: AS Dukla Praha | ||||
| 1st(1st leg) | Jeunesse Esch | - | IFK Göteborg | 1:2 (1:1) | ||
| 2nd (2nd leg) | IFK Göteborg | - | Jeunesse Esch | 0:1 (0:1) | ||
| 1st(1st leg): 14/09/1958 | 2nd (2nd leg): 30/09/1958 | Winner: IFK Göteborg | ||||
| 1st(1st leg) | Ards FC | - | Stade Reims | 1:4 (0:3) | ||
| 2nd (2nd leg) | Stade Reims | - | Ards FC | 6:2 (5:2) | ||
| 1st(1st leg): 14/09/1958 | 2nd (2nd leg): 30/09/1958 | Winner: Stade Reims | ||||
| 1st(1st leg) | SC Wismut Karl-Marx-Stadt | - | Petrolul Ploieşti | 4:2 (2:1) | ||
| 2nd (2nd leg) | Petrolul Ploieşti | - | SC Wismut Karl-Marx-Stadt | 2:0 (1:0) | ||
| 1st(1st leg): 17/09/1958 | 2nd (2nd leg): 28/09/1958 | Winner: Petrolul Ploieşti | ||||
| 1st(1st leg) | Atlético Madrid | - | Drumcondra Dublin | 8:0 (2:0) | ||
| 2nd (2nd leg) | Drumcondra Dublin | - | Atlético Madrid | 1:5 (0:3) | ||
| 1st(1st leg): 17/09/1958 | 2nd (2nd leg): 01/10/1958 | Winner: Atlético Madrid | ||||
| 1st(1st leg) | Polonia Bytom | - | MTK | 0:3 (0:0) | ||
| 2nd (2nd leg) | MTK | - | Polonia Bytom | 3:0 (1:0) | ||
| 1st(1st leg): 17/09/1958 | 2nd (2nd leg): 01/10/1958 | Winner: MTK | ||||
| 1st(1st leg) | Juventus | - | Wiener Sport-Club | 3:1 (1:1) | ||
| 2nd (2nd leg) | Wiener Sport-Club | - | Juventus | 7:0 (3:0) | ||
| 1st(1st leg): 24/09/1958 | 2nd (2nd leg): 01/10/1958 | Winner: Wiener Sport-Club | ||||
| 1st(1st leg) | DOS Utrecht | - | Sporting CP | 3:4 (0:2) | ||
| 2nd (2nd leg) | Sporting CP | - | DOS Utrecht | 2:1 (0:0) | ||
| 1st(1st leg): 01/10/1958 | 2nd (2nd leg): 08/10/1958 | Winner: Sporting CP | ||||
| decisive matches | ||||||
|---|---|---|---|---|---|---|
| FC Schalke 04 | - | KB København | 3:1 (0:0) | |||
| SC Wismut Karl-Marx-Stadt | - | Petrolul Ploieşti | 4:0 (2:0) | |||
| IFK Göteborg | - | Jeunesse Esch | 5:1 (1:1) | |||
