We study the solar wind-geomagnetic activity coupling by analyzing time series of vBSouth and AL data in the period of December 29--31, 1974. We construct state-space models whose parameters are adjusted so that when their input is vBSouth their output is as close to AL as possible and find that nonlinear models are significantly more accurate than linear models in short-term predictions. Because the real dynamics is unknown, we measure the degree of nonlinearity indirectly as the number of geomagnetic/solar wind events required to make the best prediction. Linear models are related to large event numbers, comparable to the size of the database (>40 k of samples, or 2 months of data). Small numbers of events (values between 10 and 100 are typical) correspond to nonlinear models. Model performance is measured by the short-term time-averaged prediction error. Nonlinear models have consistently lower prediction error than linear ones, often by as much as an order of magnitude. In testing the above result (1) we show that conclusions regarding model nonlinearity are biased if the prediction error is averaged over many prediction runs with different levels of activity. When we average over activity level, nonlinear and linear models appear to be equally accurate. (2) There is a range of prediction times over which linear and nonlinear models are adequately separated in accuracy. However, the models are similarly accurate if the prediction time is too short (such as 1--2 min, when the models fit high-frequency effects and noise) or for long prediction times (>1 hour, when the prediction error stops increasing). (3) The model nonlinearity is an indication for nonlinearity in the physical coupling. We show that two alternative explanations, namely nonstationarity and non-Gaussian nature of the data, are not sufficient: nonlinear models predict better even after we suppress these properties in the data. (4) The prediction error depends on the location in the state-input space, or roughly, on the activity level. In conclusion, this study further confirms the nonlinear character of the vBSouth-AL coupling.¿ 1996 American Geophysical Union