Abstract We consider hostile conflicts between two multi‐agent swarms. First, we investigate the complex nature of a single pursuer attempting to intercept a single evader (1P‐1E), and establish some rudimentary rules of engagement. We elaborate on the stability repercussions of these rules. Second, we extend the modelling and stability analysis to multi‐agent swarms with conflicting interests. The present document considers only swarms with equal membership strengths for simplicity. This effort is based on a set of suggested momenta deployed on individual agents. Because pursuers and evaders differ in the influences that they exert on one another, we emphasize asymmetry in momenta between the two types of swarm members. The proposed centralized control law evolves from a Lyapunov concept. Swarm interactions are modelled in two phases: the approach phase during which the two swarms act like individuals in the 1P‐1E interaction; and the individual pursuit phase where each pursuer is assigned to an evader. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society