This paper investigates the distributed containment tracking control problem for first-order agents with multiple dynamic leaders under directed Markovian switching network topologies. The control input of each agent can only use its local state and the states of its neighbors corrupted by white noises. Firstly, when the dynamic leaders' velocities have some special forms, which include the stationary leaders as a special case, some necessary and sufficient conditions are presented for the containment tracking in the asymptotic unbiased mean square sense. Secondly, for more general leaders' velocities, necessary and sufficient conditions are provided for the containment tracking with bounded errors in the mean square sense. Finally, a simulation example is given to illustrate the performance of the proposed control scheme. (C) 2014 Elsevier Ltd. All rights reserved.