A class of nonlinear boundary layers in a hydromagnetic flow under differential rotation is analysed. The function of these layers is to provide smooth transition from the conditions within the electrically conducting container to those in the region far away from the boundary through the flow regime. The structure of the double-decker boundary layer depends on the diffusivity of the fluid, the conductance of the rigid boundary and the relative strength of the applied magnetic field. The method of multiple scales is used to obtain uniformly valid solutions with the conductance of the container varying from zero to infinity. It is found that even a small differential rotation (ε → 0) can induce perturbations of order ε½ or of order unity in the field functions.