<p>We consider a nonlinear pursuit problem involving a group of pursuers and a single evader located initially at the origin. Players’ capabilities are defined by compact subsets of Euclidean space, and in the case of pursuers sets are finite. In order to construct a control, pursuers can only use information about values of phase coordinates of the players at the partition points of a finite time interval. At the same time, no restrictions are placed on the information used for the evader. For this reason, the pursuit goal is defined as the convergence of at least one of pursuers to the evader by any small predetermined distance for a finite time. Herewith, pursuers use piecewise constant strategies, and the evader uses a piecewise program strategy. Dynamics of each player is defined by its own system and it is assumed that the velocity vectors of each pursuer at zero form a one-sided set. A case with a single pursuer is considered separately. Sufficient conditions for the existence of initial positions of pursuers, from which the capture in a given sense takes place, are obtained for this problem.</p>