Singularities are considered in the solution of the laminar boundary-layer equations at a position of separation. A singularity of the typo here considered occurred in a careful numerical computation by Hartree for a linearly decreasing velocity distribution outside the boundary layer; it may occur generally. Whenever it does occur, the boundary-layer equations cease to be valid at and near separation on the upstream side, and also downstream of separation. The work suggests that singularities may arise in the solution of non-linear parabolic equations due to their non-linearity. The formulae found may help computers of laminar boundary layers, who desire more than a rough solution, to have an end-point at which to aim.