The three-dimensional boundary layer flow defined by the external irrotational velocity components U = x (ξ), V = αη, where α is a small positive parameter, is investigated with the aid of the boundary layer equations of Howarth. When X(ξ) = ξm a solution exact to the first power in α is found. A Pohlhausen method is then developed for any function x (ξ) and applied to the cases in which x (ξ) = ξm and x (ξ)=i-ξ.