Abstract. The game problem of pursuit is studied for dynamic processes evolving under uncertainty and counteraction. The terminal set is supposed to be a cylindrical set-valued mapping. The method of resolving functions is used to derive the sufficient conditions for the game termination in the class of quasi- and stroboscopic strategies for various schemes of the method. The guaranteed times are compared. The results are illustrated using the model with integral control unit and game problems with simple motion.

Keywords: nonstationary differential game, stroboscopic strategy, Caratheodory condition, multivalued mapping, Pontryagin condition, measurable selector, Lappo-Danilevskii condition, Minkowski functional, Cauchy formula.