This paper deals with the study of the nonlinear dynamic behaviour of 2-axle freight wagons in curves, considering the case of one single wagon (neglecting inter-car coupling forces) and of multiple wagons interacting through the buffers and the couplers. A multi-body model of a single wagon and of a three-car assembly is introduced, paying particular attention to the nonlinear and nonsmooth modelling of the suspensions and of the inter-car coupling elements. Using this model, a numerical analysis of the steady-state solution reached after the negotiation of curve transition is presented and bifurcations are identified for some particular values of the curve radius. For the single car case, it is shown that depending on the curve radius and the vehicle speed the carbody may experience severe periodic oscillations at speeds lying in the operating range of the vehicle. For the car-assembly case, it is shown that the coupling forces exchanged by the wagons significantly affect their dynamics in a curve, reducing the amplitude of vibration.