In this paper, the dynamic behaviors of a two-link hopping robot with two stopper mechanisms are investigated theoretically. In the theoretical analysis, the dynamic behaviors of the two-link hopping robot with two stopper mechanisms are modeled by use of the four phases (phase-A, phase-B, phase-C, phase-D). At the moment when the first joint stops, the state of the system transfers from phase-A to phase-B. Then, at the moment when the second joint stops, the state of the system transfers from phase-B to phase-C. In phase-C, the two-link hopping robot moves in space, and at the moment when the two-link hopping robot lands, the state of the system transfers from phase-C to phase-D. Using the principle of the conservation of momentum and angular momentum, the initial states in the periods of phase-B and phase-C are derived, and the equations of motion of the two-link hopping robot in all phases are obtained. Furthermore, the numerical simulations have been carried out, and it is confirmed theoretically that the hopping and moving action can be performed successfully.