In order to study the effect of damping failure on the dynamic stability of car-trailer combinations, the coupling between the horizontal and vertical dynamics of the CTC are investigated with a derived nonlinear extended single-track model. A damper model describing a specific damping failure phenomenon of the suspension shock absorbers is proposed as well. Using the Hopf theorem and phase portraits, the effect of a sudden damper failure on the CTC stability is analyzed via numerical simulations. The simulation results show that the bifurcation occurs at a specific longitudinal velocity and the damping failure has effect on the system dynamic stability, i.e. the system dynamic critical speed.