In this paper we examine further the physics of vortex axisymmetrization, with the goal of elucidating the dynamics of outward-propagating spiral bands in hurricanes. The basic physics is illustrated most simply for stable vorticity monopoles on an f-plane. Unlike the dynamics of sheared disturbances in rectilinear shear flow, axisymmetrizing disturbances on a vortex are accompanied by outward-propagating vortex Rossby-waves whose restoring mechanism is associated with the radial gradient of storm vorticity. Expressions for both phase and group velocities are derived and verified; they confirm earlier speculations on the existence of vortex Rossbywaves in hurricanes. Effects of radially propagating vortex Rossby-waves on the mean vortex are also analysed. In conjunction with sustained injection of vorticity near the radius of maximum winds, these results reveal a new mechanism of vortex intensification. The basic theory is then applied to a hurricane-like vortex in a shallow-water asymmetric-balance model. The wave mechanics developed here shows promise in elucidating basic mechanisms of hurricane evolution and structure changes, such as the formation of secondary eye-walls. Radar observations possessing adequate temporal resolution are consistent with the predictions of this work, though more refined observations are needed to quantify further the impact of mesoscale banded disturbances on the evolution of the hurricane vortex.* Linear contour dynamical models cannot predict such effects since the sheared disturbance-component residing between contours is neglected.