The same basic mechanism is responsible for asymmetric drainage of thin circular films and marginal regeneration in vertical, rectangular films. 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 the 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-1-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.