I define multi-stage stochastic games in continuous time. As in Bergin and MacLeod (1993), strategies have infinitesimal inertia, i.e., agents cannot change their strategies in an infinitesimal interval immediately after each time t. I extend the framework to allow for mixed strategies. As a novel feature in continuous time, mixing can be done both over actions, and over time (choosing the time of the action). I also define ”layered times,” which allow for stopping the clock and having various stages of the game be played at the same moment in time. I apply the theory to a trading game, where patient agents can choose whether to trade immediately or place a limit order and wait.