A method is presented that allows fatigue life predictions on the basis of creep life data. The approach is based on the assumption that the time-dependent failure of polymers is determined by the intrinsic strain softening that is initiated when a critical threshold value of the plastic strain is surpassed. To facilitate fatigue predictions, an acceleration factor is defined that indicates how much faster plastic strain is accumulated by a cyclic signal compared to its static mean stress. Analytical solutions of the acceleration factor are presented for triangular and square waves, which predict that only the stress amplitude of the cyclic signal and the material's stress dependency affect fatigue life, whereas frequency plays no role. Verification using several glassy and semicrystal line polymers demonstrates that this method yields accurate quantitative lifetime predictions not only for polymers that exhibit ductile failure but also for those that display brittle fracture, provided that fracture is preceded by (localized) plastic flow.