We propose a general discrete time model for multilevel event history data. The model is developed for the analysis of longitudinal repeated episodes within individuals where there are multiple states and multiple types of event (competing risks) which may vary across states. The different transitions are modelled jointly to allow for correlation across transitions in unobserved individual risk factors. Implementation of the methodology using existing multilevel models for discrete response data is described. The model is applied in an analysis of contraceptive use dynamics in Indonesia where transitions from two states, contraceptive use and nonuse, are of interest. A distinction is made between two ways in which an episode of contraceptive use may end: a transition to nonuse or a switch to another method. Before adjusting for covariate effects, there is a strong negative residual correlation between the hazards of a transition from use to nonuse and from nonuse to use; this correlation is due to a tendency for short periods of nonuse after a birth to be followed by long periods of using the same contraceptive method.