Abstract. This article considers the problem of detecting break points for a nonstationary time series. Specifically, the time series is assumed to follow a parametric nonlinear time-series model in which the parameters may change values at fixed times. In this formulation, the number and locations of the break points are assumed unknown. The minimum description length (MDL) is used as a criterion for estimating the number of break points, the locations of break points and the parametric model in each segment. The best segmentation found by minimizing MDL is obtained using a genetic algorithm. The implementation of this approach is illustrated using generalized autoregressive conditionally heteroscedastic (GARCH) models, stochastic volatility models and generalized state-space models as the parametric model for the segments. Empirical results show good performance of the estimates of the number of breaks and their locations for these various models.