Traditional single-agent search algorithms usually make simplifying assumptions (single search agent, stationary target, complete knowledge of the state, and sufficient time). There are algorithms for relaxing one or two of these constraints; in this paper we want to relax all four. The application domain is to have multiple search agents cooperate to pursue and capture a moving target. Agents are allowed to communicate with each other. For solving Multiple Agents Moving Target (MAMT) applications, we present a framework for specifying a family of suitable search algorithms. This paper investigates several effective approaches for solving problem instances in this domain.