An analysis of equilibrium boundary layers based on the Schofield–Perry defect law, which applies to flow in a moderate to strong adverse pressure gradient, is presented. The conditions derived for self-preserving or equilibrium boundary layers differ from those given by previous analyses based on the usual velocity-defect law. It is shown that twelve observed boundary layers on smooth walls conform to these new conditions for precise equilibrium flow. As the analytical expression for the Schofield–Perry defect law does not vary with pressure gradient, a specific expression for the shear-stress profile in any equilibrium layer can be derived. The predicted shear-stress profiles show good agreement with experimental data. Limits for the flow parameters within which equilibrium layers can exist are derived, and it is shown that observed equilibrium layers fall within these limits. A prediction method for layers in smoothly changing adverse-pressure gradients is outlined and demonstrated using equilibrium data. The unified account of equilibrium flow in adverse pressure gradients presented here is used to resolve some disagreements in the literature concerning existence conditions for equilibrium boundary layers.