This paper presents a bifurcation analysis for car-trailer lateral stability considering the variation of forward vehicle velocity. As an important aspect in car-trailer dynamics, the lateral stability has a strong influence on the overall vehicle safety. To increase car-trailer safety, it is vital to estimate the lateral stability region. With respect to single-unit vehicles, such as cars and trucks, Car-Trailer Systems (CTSs) exhibit unique dynamic features, including unstable motion modes, namely, jack-knifing, trailer sway and rollover. Thus, we perform a sensitivity analysis using Lyapunov stability theory to evaluate the nonlinear stability features of a CTS. To this end, a 6 Degrees of Freedom (DOF) nonlinear car-trailer model is generated, which is a non-autonomous system at different forward velocity. The nonlinear stability analysis paves the road for developing active safety systems for CTSs.