In this paper we present a method to anticipate periodic movements in a multi-agent reactive context, of which a typical example is the guard who patrols. Our system relies on a dynamic modeling of motion, based on a state anticipation method. This modeling is achieved with an incremental learning algorithm, dedicated to 3D real time environments. We analyze the performance of the method and demonstrate its usefulness to improve the credibility of pursuit and infiltration behaviors in front of patrolling agents.