The objective of this study is to obtain optimal cyclic gaits for a biped robot without actuated ankles. Two types of motion are studied: walking and running. For the walking, the gait is composed uniquely of successive single support phases and instantaneous double support phases that are modelled by passive impact equations. The legs swap their roles from one single support phase to the next one. For the running, the gait is composed of stance phases and flight phases. A passive impact with the ground exists at the end of flight. During each phase the evolution of m joints variables is assumed to be polynomial functions, m is the number of actuators. The evolution of the other variables is deduced from the dynamic model of the biped. The coefficients of the polynomial functions are chosen to optimise criteria and to insure cyclic motion of the biped. The chosen criteria are: maximal advance velocity, minimal torque, and minimal energy. Furthermore, the optimal gait is defined with respect to given performances of actuators: The torques and velocities at the output of the gear box are bounded. For this study, the physical parameters of a prototype, which is under construction, are used. Optimal walking and running are defined. The running is more efficient for high velocities than the walking with respect to the studied criteria.