Аннотация:A game problem is considered in which several controlled objects pursue one evader. A general scheme for obtaining sufficient solvability conditions for the pursuit problem is proposed, one that makes it possible to investigate games with equal or different player response properties ( ″inertia″ ). Two examples that illustrate the following situation are cited: if each of the pursuers cannot catch the evader, then by acting in coordination they can achieve the goal over a finite time.