The stability of laminar boundary layers at separation is considered. The velocity distribution is represented by (1) a Pohlhausen fourth-degree polynomial P4, and (2) by a Falkner—Skan similarity profile at separation, Hartree β = − 0. 1988. The Orr—Sommerfeld equation is integrated using Runge—Kutta with Gram—Schmidt orthonormalization. Using single precision arithmetic, the method leads to satisfactory answers at Reynolds numbers R1 = 100 000 and larger. In either case the minimum critical Reynolds number is found to be of the order of 100. It is found that the neutral curves for the P4 profile obtained by solving the Orr—Sommerfeld equation, whether exactly (numerically) or within the framework of the asymptotic approximations, approach along the upper branch the same asymptotic value, namely α1 = 0.8028 (in the case of the β = − 0. 1988 profile, however, the corresponding values is α1 = 1.240). It is also found that the asymptotes to the lower branch in both cases vary with α1 according to R11/3∼α1 −7/9 (in the case of the β = − 0. 1988 profile however, the corresponding variation is R11/3 ∼ α1 - 0. 477).