We investigate the influence of flow rate and rotation on the structure and response of burner-stabilized spherical premixed flames. Asymptotic methods are employed in which we exploit the limit of large activation energy to resolve the reaction zone structure, and a perturbation analysis is carried out for small rates of rotation. We first construct the leading order solution, which describes a stationary (nonrotating) spherical dame. This configuration is analyzed to determine extinction characteristics, and the various mechanisms for stabilization of curved flames are also identified. Rotation is then included as a perturbation, and closed form solutions of the appropriate governing equations are obtained. We find that a secondary flow is induced inward toward the burner poles and outward from the equator. This in turn deforms the flame into a pancake shape that may he flattened either at the poles or the equator, depending on the combined effects of Lewis number, flame stretch, and ambient temperature. We also present results for the related problem of a rotating monopropellant droplet in the Appendix.