In this paper, the dynamic behaviors of a two-joint articulated hopping robot with two stopper mechanisms are theoretically investigated. In the theoretical analysis, the four phases are used to model the dynamic behaviors of the two-joint articulated hopping robot. By the use of the principle of the conservation of momentum and angular momentum, the initial states in the periods of the phase-B and the phase-C are derived, and the equations of motion of the two-joint articulated hopping robot in the four phases are obtained. Furthermore, the numerical simulations have been carried out, and it is theoretically confirmed that the hopping and moving actions can be successfully performed.