Stratford's method of computing the development of a turbulent boundary layer in a strong adverse pressure gradient, based on division of the layer into an inner equilibrium layer and an outer layer of almost constant total-head, is simple and is based on current knowledge of the properties of turbulent flows, but the correspondence with experiment is worse than would be expected. The causes of this are investigated, first by testing the basic assumptions against the measurements of Schubauer & Klebanoff and then by calculating from the theory properties of the layer at intermediate stages of the development towards separation. It is shown that the theoretical condition for zero wall stress (a relation between pressure rise and pressure gradient) is always satisfied twice, first at an intermediate stage of development with wall stress about one-fifth of the initial value and second at the real position of zero stress. This behaviour involves a rapid decrease of pressure gradient in the neighbourhood of separation, caused by rapid thickening of the layer, and it is shown that the pressure distribution near separation depends only on the pressure rise to separation and the characteristics of the initial boundary layer and not on the geometry of the flow. With more measurements of boundary layers separating in strong adverse pressure gradients, these characteristic distributions could be determined as a one-parameter family. Their use for the prediction of position and pressure rise to separation in flows with specified boundaries without prior knowledge of the pressure distribution is discussed.