We consider hostile conflicts between two multi-agent swarms, called pursuers and evaders. A Newtonian dynamics-based double integrator model is taken into account, as well as a control strategy using the relative positions and velocities of opposing swarm members. This control is introduced to achieve stability and the capture of the evaders by the pursuers. The present document considers only swarms with equal membership strengths and equal mass for simplicity. This effort begins with a set of suggested interaction force profiles, which are functions of local vectors. To formulate a robust control law, a Lyapunov-based stability analysis is used. The group pursuit is conceived in two phases: the approach phase, during which the two swarms act like two individual agents, and the assigned pursuit phase, where each pursuer has an assigned evader. We show that the uncontrolled dynamics, which are marginally stable, are stabilized by the new controller.