  We provide a systematic derivation of boundary layer models in
magnetohydrodynamics (MHD), through an asymptotic analysis of the
incompressible MHD system. We recover classical linear models, related to the
famous Hartmann and Shercliff layers, as well as nonlinear ones, that we call
magnetic Prandtl models. We perform their linear stability analysis,
emphasizing the stabilizing effect of the magnetic field.
