To the problem of Chernous'ko

The problem of simple pursuit of one evader by the group of pursuers is studied, provided that among the pursuers there are both members, the maximum speeds of which coincide with the maximum speed of the evader, and participants whose maximum speeds are strictly less than the maximum speed of the evader, while the evader does not leave a convex polyhedral set. The conditions under which the pursuers with fewer capabilities do not affect the solvability of problem of evasion are obtained.