An analytical theory is developed for a class of stable quasi-geostrophic vortices propagating either in the westward direction with supercritical velocities (c<−βR2d) or eastward, where Rd is the radius of deformation and β is the gradient of the Coriolis parameter. The numerical spectral calculations, initiated by the theoretical solutions, indicate that the supercritical vortices move initially with the predicted velocity, but later slow down to the speed of the long planetary waves. The period of time during which an eddy is propagating with its initial velocity is analysed as a function of its strength and (initial) speed. The theoretical solution has a distinctive streamline signature (‘alpha gyre’), which also appears in the final state of the numerical calculations, including those for an initially completely symmetric vortex placed on the β-plane.