This paper treats the problem of railway vehicle dynamics in transition curves at velocities around critical velocity. The authors remain shortly results they obtained so far. Based on that they justify scope and aims of the current studies discussed in the paper. Consequently, the main subject of studies in the paper are 2-axle railway vehicles. Two examples of 2-axle freight cars were selected and studied with their dynamical models and the corresponding simulation software. The main difference between both models is laden and empty state of vehicle. Selected simulation results are included in the paper and discussed. In conclusions generally more predictable behaviour of 2-axle vehicles is stated as compared to 4-axle ones and bogies. Despite it the intriguing, unexpected non-linear features were revealed in case of the empty car.