Threshold autoregressive self-exciting open-loop (TARSO) models are fitted to six time series of water table depths with precipitation excess as input variable. Basically, these models are nonlinear in structure because they incorporate several regimes which are separated by so-called thresholds. For each well a subset TARSO ((SS)TARSO) model is selected using a Bayes information criterion (BIC). (SS)TARSO models are used to simulate realizations of water table depths with lengths of 30 years, from which characteristics such as durations of exceedance are computed. The simulation performance of the fitted (SS)TARSO models is compared with results obtained from transfer function noise (TFN) models, dynamic regression (DR) models, and with a physical descriptive model, called SWATRE, extended with additional autoregressive moving average (ARMA) processes for the noise (SWATRE+ARMA). As compared to the linear TFN and DR models the (SS)TARSO models perform better because they incorporate several regimes. These regimes are the result of different soil layers or drainage levels. Furthermore, it is interesting that (SS)TARSO models show a good relative performance as compared to the SWATRE+ARMA models. A possible reason may be that inputs of SWATRE are uncertain. ¿ 1999 American Geophysical Union