Measurements in three boundary layers, one with constant free-stream velocity and two with power-law variations of free-stream velocity giving ‘moderate’ and ‘strong’ adverse pressure gradients, are presented and discussed. Several unifying features of the turbulent motion, expected to appear in all boundary layers not too far from equilibrium, are identified. The intensity spectra at higher wavenumbers follow the Kolmogorov inertial-subrange law, although the Reynolds number is not particularly high even by laboratory standards: in addition the smaller-scale motion in the outer layer is determined entirely by the local shear stress and the boundary-layer thickness. The large eddy motion increases in strength relative to the general turbulence level as the general turbulence level increases, and the limited evidence available suggests that the large eddies are similar to those in the free mixing layer. In all cases the large eddies contribute a significant proportion of the shear stress in the outer layer.