At high supersonic flight speeds or with a highly cooled surface, there is a strong density gradient across the boundary layer. Close to the surface the gas is cool and of low-temperature molecular weight; at the outer edge of the boundary layer the gas is hot and may be partially dissociated, so that its density is lower by a factor of 10 - 20. At the same time a strong centrifugal acceleration is produced by the body curvature, and this outward acceleration acts in the direction of decreasing density. The question arises as to whether this destabilizing effect of the acceleration field in a density gradient is sufficient to overcome the stabilizing effect of the increasing angular momentum of the fluid in the outward direction. The conclusion is drawn that the strong stabilizing effect of the outward increase in angular momentum is always dominant in the laminar boundary layer. (Author).