An interpretative analysis of experimental results on the failure of synthetic fibers in fatigue under cyclic tension leads to the conclusion that rupture is of a brittle nature. Although molecular rearrangement undoubtedly takes place during longitudinal fatiguing, rupture itself cannot be regarded as a viscous, laminar flow process. Failure is localized; the undamaged sections of the specimens show relatively less important effects of the fatiguing. Lifetime cannot be predicted from measurements of fiber tenacity, modulus, or rate of creep. A theory of fatigue rupture, based on the observation of cracks in specimens strained to breakage, is formulated. The treatment involves the assumption that a crack grows by a nucleation process up to a critical size. At a slightly larger size, the crack becomes unstable and propagates spontaneously, to produce rupture. The theory leads to an expression for lifetime as a function of stress that is in substantial agreement with experimental data on a number of samples.