Abstract: The concepts of linearity, nonlinearity and real critical speeds for railway vehicles are introduced in the first part of this paper. Then a nonlinearmathematical model for a railway freight carwith 31 degrees of freedom is set up, inwhich the nonlinearity arising fromthe friction forces andwheel/rail interactions are considered. Numerical method is used to investigate the hunting stability behaviors of the freight car, including the limit cycles, quasi-periodic solutions and chaos in the system.