We introduce a notion of subgames for stochastic timing games and the related

notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of

subgame-perfect equilibrium for continuous-time games is not available in general, we argue

that our model is the appropriate version for timing games. We show that the notion coincides

with the usual one for discrete-time games. Many timing games in continuous time have only

equilibria in mixed strategies – in particular preemption games, which often occur in the

strategic real option literature. We provide a sound foundation for some workhorse equilibria

of that literature, which has been lacking as we show. We obtain a general constructive

existence result for subgame-perfect equilibria in preemption games and illustrate our findings

by several explicit applications.