The dynamic inflation of hyperelastic spherical membranes of a Mooney-Rivlin material is analyzed in this study. Various inflation regimes are identified through ranges of the material parameters and driving pressure. In particular, the conditions for oscillatory inflation around the static fixed point are examined. It is found that, for a given material, the frequency of oscillation exhibits a maximum at some pressure level, which tends to increase for materials closer to neo-Hookean behavior.