In this article the three-dimensional laminar boundary layer with a rapidly oscillating external flow is discussed, because the problems in which the oscillations are superimposed on a stream are much more important in applications. Containing the supplementary components $Q_1$ and $Q_2$ of the pressure gradient, depending even of the normal coordinate n, the mean flow in our case differs considerably compared to the classical steady case. First, an approximate method to calculate both longitudinal and transverse velocity components of the mean flow is established. Then the method is applied to study the boundary layer (velocity, thickness, separation) on a sphere.