Drainage of circular foam films is much more rapid when the drainage is asymmetric. The same basic mechanism is responsible for asymmetric drainage of thin circular films and marginal regeneration. A linear stability analysis showed that these phenomena are caused by a hydrodynamic instability that is produced by a surface-tension-driven flow and stabilized by surface viscosity, surface diffusivity and system length scale. A criterion for the onset of this instability was derived. Experiments performed on small circular films of aqueous solutions of SDS and SDS:l-dodecanol demonstrated the strong stabilizing effect of surface viscosity. Experimental results were found to be in good agreement with the predictions of the linear stability analysis. Finite difference simulations demonstrate the validity of the linear stability analysis for when the radius of curvature of the “barrier ring” is large compared to the transverse wave length of the instability. These simulations also show the circulation cells that relax the surface tension gradient and thus accelerate the drainage of the film.