Abstract. The paper studies problems of differential games of group pursuit with integral constraints on the controls of players such as the Pontryagin control example and simple pursuit for the case of l-catch. The problems are solved on the basis of Chikrii’s method of resolving functions. The structure of resolving function is proposed, which substantiates the parallel approach strategy, i.e., the П-strategy for pursuers. New sufficient solvability conditions for problems of group pursuit are obtained.

Keywords: Pontryagin’s control example, simple pursuit, integral constraint, unknown function, parallel approach strategy, l-catch.