I Won't Run Away by Alvin Stardust first appeared on the Israeli foreign-music chart on 9 Dec 1984, entering at #17. It peaked at #12 on 30 Dec 1984. In total it spent 5 weeks on the chart, last charting on 13 Jan 1985.
| Wk | Date | Pos |
|---|---|---|
| 1 | 9 Dec 1984 | 17 |
| 2 | 16 Dec 1984 | 14 |
| 3 | 30 Dec 1984 | 12 |
| 4 | 6 Jan 1985 | 19 |
| 5 | 13 Jan 1985 | 30 |