The definition of the evolutionary stable strategies (ESS) used in works on the positional game theory possesses one shortage for the dynamic game: at the repeated application of ESS in component games it is not necessary that ESS be in the basic game. The new definition of ESS allowing to save from this shortage has been proposed. It consists in adding the second ESS demand for measures generated in game sets for corresponding behavior strategies. For the differential game this condition has been reduced to the fact that the trajectories in the basic game and the repeated one must be no coinciding.