The rapid time variation of mobile radio channels is often modeled as a random process with second order moments reflecting vehicle speed, bandwidth and the scattering environment. These statistics typically show that there is little room for prediction of channel properties such as received power or complex taps of the impulse response coefficients, at least when linear predictor structures are considered. We have used mutual information estimation to measure statistical dependencies in sequences of wideband mobile radio channel data and found significant nonlinear dependencies, far exceeding the linear component. Based on these upper limits for the predictability of channel evolution over time intervals up to 30 ms ahead, we study practical nonlinear predictor systems using Multivariate Adaptive Regression Splines (MARS) and Quadratic Volterra Filters.