This paper addresses the problem of pursuit of a maneuvering target by a group of pursuers distributed in the plane. This group pursuit problem is solved in a distributed way by employing a relay pursuit strategy, that is, a group pursuit scheme, such that at each instant of time, only one pursuer is assigned the task of capturing the maneuvering target. During the course of the relay pursuit, the pursuer-target assignment changes dynamically with time in accordance with the (time-varying) proximity relations between the pursuers and the target. Simulation results are presented to highlight the theoretical developments.