Interruption of periodic wave propagation by the nucleation and subsequent disintegration of spiral waves is thought to mediate the transition from normal sinus rhythm to ventricular fibrillation. This sequence of events may be precipitated by a period doubling bifurcation, manifest as a beat-to-beat alternation, or alternans, of cardiac action potential duration and conduction velocity. How alternans causes the local conduction block required for initiation of spiral wave reentry remains unclear, however. In the present study, a mechanism for conduction block was derived from experimental studies in linear strands of cardiac tissue and from computer simulations in ionic and coupled maps models of homogeneous one-dimensional fibers. In both the experiments and the computer models, rapid periodic pacing induced marked spatiotemporal heterogeneity of cellular electrical properties, culminating in paroxysmal conduction block. These behaviors resulted from a nonuniform distribution of action potential duration alternans, secondary to alternans of conduction velocity. This link between period doubling bifurcations of cellular electrical properties and conduction block may provide a generic mechanism for the onset of tachycardia and fibrillation.