The zero dynamics of a hybrid model of bipedal walking are introduced and studied for a class of N-link, planar robots with one degree of under actuation and outputs that depend only on the configuration variables. Asymptotically stable solutions of the zero dynamics correspond to asymptotically stabilizable orbits of the full hybrid model of the walker. The Poincaré map of the zero dynamics is computed and proven to be diffeomorphic to a scalar, linear, time-invariant system, thereby rendering transparent the existence and stability properties of periodic orbits.