  In this paper we investigate a differential game in which countably many
dynamical objects pursue a single one. All the players perform simple motions.
The duration of the game is fixed. The controls of a group of pursuers are
subject to geometric constraints and the controls of the other pursuers and the
evader are subject to integral constraints. The payoff of the game is the
distance between the evader and the closest pursuer when the game is
terminated. We construct optimal strategies for players and find the value of
the game.
