This paper examines the problem of transitioning between gaits using a sagittal-plane reduced-order model of quadrupedal running, which has compliant elements in its torso and legs. First, periodic motions that correspond to pronking and two variations of bounding are generated. Analysis of the torso pitch motion in these gaits reveals basic differences that determine whether transitions between these gaits can be achieved. This observation is then incorporated in control design to enhance the stability of the generated motions. The domain of attraction of the closed-loop systems is estimated through simulation, showing that transition between pronking and bounding can be realized as a sequence of switchings between fixed points. The results in this work can be regarded as the first step towards synthesizing controllers for gait transitions within template models for quadrupedal running gaits.