This paper focuses on the identification of nonlinear hybrid systems involving unknown nonlinear dynamics. The proposed method extends the framework of [1] by introducing nonparametric models based on kernel functions in order to estimate arbitrary nonlinearities without prior knowledge. In comparison to the previous work of [2], which also dealt with unknown nonlinearities, the new algorithm assumes the form of an unconstrained nonlinear continuous optimization problem, which can be efficiently solved for moderate numbers of parameters in the model, as is typically the case for linear hybrid systems. However, to maintain the efficiency of the method on large data sets with nonlinear kernel models, a preprocessing step is required in order to fix the model size and limit the number of optimization variables. A support vector selection procedure, based on a maximum entropy criterion, is proposed to perform this step. The efficiency of the resulting algorithm is demonstrated on large-scale experiments involving the identification of nonlinear switched dynamical systems.