In this paper we present the results of a numerical investigation of the lateral dynamics of a model of a railway bogie rolling on a straight and perfect track without irregularities. A nonlinear online wheel/rail contact relationship is used in this model. The suspension elements have linear characteristics. The S1002CN wheel profile and the CHN60 rail profile are applied into the calculation of the dynamic wheel/rail contact relationship. The speed of the bogie is selected as the control parameter and all other parameters are kept constant. In order to investigate different motions appearing in the system, we compute time series, return maps, and phase portraits.