This paper presents a general delay swarm model to study the collective behavior of a group of autonomous agents in the presence of communication delays. It is proved that under certain conditions the swarm members will converge to a finite region around the swarm center and move together in a cohesive cluster following the motion of the center. For general cases, the delay swarm may display more complex dynamics, including oscillation and divergence, depending on the delay values. This suggests that the time delay may have significant consequence in the collective dynamics of swarms.