Prediction error learning algorithms for neural state space models are developed, both for the deterministic case and the stochastic case with measurement and process noise. For the stochastic case, a predictor with direct parametrization of the Kalman gain by a neural net architecture is proposed. Expressions for the gradients are derived by applying Narendra’s sensitivity model approach. Finally a linear fractional transformation representation is given for neural state space models, which makes it possible to use these models, obtained from input/output measurements on a plant, in a standard robust performance control scheme.