In this paper it is demonstrated that pronking (or trotting or pacing) is the preferred mode of behavior of a fairly generic quadruped model. This gait often occurs even though no explicit control is used to force it, and thus the system is said to "self-organize." Further, it is demonstrated that, despite the complicated coupled nonlinear dynamics, the system is still amenable to analysis if certain parameters are assumed small, namely the leg masses and the hip spring constants. Explicit conditions are presented for a symmetric pronk. In one condition, the leg length and the hip spring constant determine the pronking height, which has implications for quadruped robot design.