In this paper, the nonlinear identification (ID) of the lateral dynamics of a road vehicle is presented. The mathematical description of lateral dynamics is crucial for developing various self-driving functions. One method of describing dynamics is system identification from measured data. During the measurements, the steering servo of a test vehicle kept in straight-line motion by a self-driving function was artificially excited. A Hammerstein–Wiener model was successfully applied for the identification of these measurements. A nonlinear estimator was used during the fitting, which needed high computing power. For the Hammerstein–Wiener model, we used the two-stage algorithm (TSA) with a bilinear estimation method, which makes it possible to apply linear regression. We compared these methods during simulations and real data.