In this paper a selection theory for stochastic games is developed. The theory itself is based on the ideas of Harsanyi and Selten to select equilibria for games in standard form. We introduce several possible definitions for the stochastic tracing procedure, an extension of the linear tracing procedure to the class of stochastic games. We analyze the properties of these alternative definitions. We show that exactly one of the proposed extensions is consistent with the formulation of Harsanyi???Selten for games in standard form and captures stationarity.