A semi‐infinite mass of incompressible, viscous, electrically conducting fluid is bounded by an infinite plane wall with a constant‐strength magnetic field perpendicular to the wall. Either the wall motion is changed indicially parallel to its surface or a constant current is discharged parallel to the surface. The fluid motion and induced magnetic field are discussed for the ratio of kinematic viscosity to magnetic diffusivity &egr; small compared to one and equal to one. For &egr; « 1, it is shown that for the indicial motion of a perfect conductor or for a current discharge there exists a thin viscous boundary layer at the wall; the diffusing Alfve´n wave region extends outside this layer.