The hydrodynamic stability of mixed convection in an annulus is studied. The linear stability limit for forced flow up a vertical annulus with a constant heat flux applied to the inner wall and the outer wall insulated is determined. The result indicates that the fully-developed flow is thermally unstable in most regions of an appropriate parameter space. The magnitudes of the finite amplitude disturbances in the unstable region are determined by utilizing Stuart's shape assumption. Distorted mean flow profiles are obtained and the increase in heat transfer rates due to these disturbances are calculated from the results and agree well with the experimental data.