The dynamic behaviour of a wheel-rail vehicle is influenced by two nonlinear effects resulting from the wheel-rail contact geometry and from the contact forces between wheel and rail. In this paper methods are presented for handling these two nonlinearities efficiently in the simulation of dynamic curving. Modelling of wheel-rail mechanics includes elastic torsion of the wheelset shaft while track elasticity is approximated by a rigid track-element having flexible connections to the roadbed. Three dimensional contact geometry is regarded, and the creep forces due to Kalker’s simplified theory are evaluated with the computer code FASTSIM or with nonlinear approximations. As an example, a four-axle wheel-rail vehicle is regarded in the simulation of curve entry and negotiation. Effects of using only two dimensional contact geometry and nonlinear approximations for the creep forces as well as influences of the introduced elastic degrees of freedom are shown in the simulation results.