The development of a turbulent boundary layer in a strong adverse pressure gradient can be described by the two-layer model proposed by Stratford (1959), in which the outer part of the flow is assumed to be unmodified by the pressure-rise and the inner part described by two local parameters, the surface stress and the pressure gradient. The description suggests that the modification of the original flow is in some sense self-preserving, and it is shown here that self-preserving development of the modification is consistent with the Reynolds equations of turbulent flow in particular pressure distributions. For these distributions, the predictions of the two-layer model are confirmed without any need to make the sharp and arbitrary distinction between the two parts of the boundary layer.