An evasion differential game of two pursuers and one evader in R 2 is studied. Unlike the traditional integral constraints, in the present work, integral constraints are imposed on each component of control functions of the players. By definition, evasion is said to be possible if the state of a pursuer does not coincide with that of the evader for all t ≥ 0. Sufficient conditions of evasion are obtained and then strategies for the evader are constructed.

A pursuit differential game of two pursuers and one evader in ℝ2 is studied. All players' controls are subjected to coordinate-wise integral constraints. By definition, pursuit is completed if the state of a pursuer coincides with that of the evader at some time. The problem is to find conditions of completion of pursuit. We show that if the energy vector of the evader belongs to a polygon, then pursuit can be completed.