The behavior of the compressible boundary layer equations close to a point of zero skin-friction is studied using a perturbation technique of Kaplun. The behavior of the skin friction is reduced to a study of a nonlinear integral equation with an Abel kernel. For a cold wall this yields the singular behavior described by Buckmaster [2] from a different point of view. For a hot wall the behavior is apparently regular when the heat transfer is non zero, in agreement with Stewartson [11]. There is no evidence that the boundary layer breaks down anywhere than at a point of zero skin friction and the implications of this for the similarity solutions of Cohen and Reshotko are discussed.