Despite the general interest in nonlinear dynamics in animal populations, plant populations are supposed to show a stable equilibrium that is attributed to fundamental differences compared with animals. Some studies find more complex dynamics, but empirical studies usually are too short and most modelling studies ignore important spatial aspects of local competition and establishment. Therefore, we used a spatially explicit individual-based model of a hypothetical, non-clonal perennial to explore which mechanisms might generate complex dynamics, i.e. cycles. The model is based on the field-of-neighbourhood approach that describes local competition and establishment in a phenomenological manner. We found cyclic population dynamics for a wide spectrum of model variants, provided that mortality is determined by local competition and recruitment is virtually completely suppressed within the zone of influence of established plants. This destabilizing effect of local processes within plant populations might have wide-ranging implications for the understanding of plant community dynamics and coexistence.