Various vibration-attenuating slab tracks have been introduced into urban railways to minimize the negative effects of train-induced ground vibration and noise. However, compared with traditional slab tracks, vibration-attenuating slab tracks usually have a lower overall stiffness, which reduces the vehicle lateral stability. This paper presents an investigation of the nonlinear hunting stability of fast metro rail vehicles traveling on vibration-attenuating slab tracks. A three-dimensional vehicle–track coupled model considering different vibration-attenuating slab tracks is developed to investigate the nonlinear hunting behavior of metro vehicles running on different elastic vibration-attenuating tracks. The nonlinear critical speed and wheelset hunting limit cycle of two types of metro vehicles traveling on four typical types of vibration-attenuating tracks are compared in detail. The influences of vehicle–track system parameters, including rail fastener stiffness and vehicle suspension parameters, on the vehicle lateral nonlinear stability are reported. The results show that the flexibility of vibration-attenuating slab tracks leads to a large wheelset limit cycle and lowers the nonlinear critical speed. Increasing track lateral stiffness and designing appropriate vehicle suspension parameters can improve the lateral stability of rail vehicles traveling on vibration-attenuating slab tracks.