Numerical solutions of the laminar, incompressible boundary-layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified; the pressure is deduced from the solution. A vorticity--stream-function formulation of the boundary-layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite-difference equations, in which the flow direction is taken into account, are obtained by several global iteration schemes which are stable and have unconditional diagonal dominance. Results are compared with Klineberg and Steger's separated boundary-layer calculations, and with Briley's solution of the Navier-Stokes equations for a separated region. In addition, an approximate technique is presented in which the streamwise convection of vorticity is set equal to zero in the reversed flow region; such a technique results in a quick forward-marching procedure for separated flows.