This document considers hostile conflicts between two swarms, called pursuers and evaders, based on a double integrator model. In order to convert the marginally stable dynamics into stable-capture behavior, we introduce a control strategy based on the relative positions and velocities of opposing swarm members. To evaluate its effectiveness, a Lyapunov-based stability analysis is performed. For simplicity, this document considers swarms with equal membership strengths and equal mass only. The modeling is based on a set of suggested interaction force profiles, which are functions of local vectors. The group pursuit is conceived in two phases: the approach phase during which the two swarms act like two individuals; and the assigned pursuit phase where each pursuer is assigned to an evader.