Predator-prey cycles rank among the most fundamental concepts in ecology, are predicted by the simplest ecological models and enable, theoretically, the indefinite persistence of predator and prey1-4. However, it remains an open question for how long cyclic dynamics can be self-sustained in real communities. Field observations have been restricted to a few cycle periods5-8 and experimental studies indicate that oscillations may be short-lived without external stabilizing factors9-19. Here we performed microcosm experiments with a planktonic predator-prey system and repeatedly observed oscillatory time series of unprecedented length that persisted for up to around 50 cycles or approximately 300 predator generations. The dominant type of dynamics was characterized by regular, coherent oscillations with a nearly constant predator-prey phase difference. Despite constant experimental conditions, we also observed shorter episodes of irregular, non-coherent oscillations without any significant phase relationship. However, the predator-prey system showed a strong tendency to return to the dominant dynamical regime with a defined phase relationship. A mathematical model suggests that stochasticity is probably responsible for the reversible shift from coherent to non-coherent oscillations, a notion that was supported by experiments with external forcing by pulsed nutrient supply. Our findings empirically demonstrate the potential for infinite persistence of predator and prey populations in a cyclic dynamic regime that shows resilience in the presence of stochastic events.