This paper studies stability properties of stochastic switched nonlinear time-delay systems. The stability analysis is based on two extensions of the Lyapunov-based method: the Krasovskii approach and the Razumikhin approach. In terms of the Krasovskii approach, Krasovskiitype stability conditions are derived based on Lyapunov-Krasovskii functions and average dwell-time condition. In terms of the Razumikhin approach, Razumikhin-type stability conditions are obtained via Lyapunov-Razumikhin functions, the small gain condition, and the fixed dwell-time condition. Furthermore, as a widespread phenomenon in switched systems, the asynchronous switching case is studied. Both Krasovskii-type and Razumikhin-type stability conditions are established for the asynchronous switching case. Finally, the developed results are illustrated via two examples from the mechanical rotational cutting process and networked switched control systems.