Abstract: We consider the pursuit problem for the so-called game “boy and crocodile”. “Boy” is moving in according to the equation ỳ = v, “crocodile” moving according to the equation ẍ = u and “boy” can not leave the closed ball of radius R > 0. Control of the pursuer is subjected to integral constraint, and the evader’s control is subjected to geometric constraint. Sufficient conditions of completion of pursuit from all initial positions are obtained.