Measurements are presented of the mean flow in a supersonic turbulent boundary layer subjected to a constant weak transverse pressure gradient. The temperature and longitudinal velocity and the axial shear stress were only slightly affected by the three-dimensionality but a clearly defined crossflow component appeared, in the manner suggested by theory and confirmed in earlier experiments. The flow deflection angle and transverse-velocity component achieved a self-preserving form so long as the transverse-pressure gradient remained constant, and both achieved a maximum at the sublayer edge; the deflection angle seemed to decrease again between the latter and the surface. An empirical relation was found between the pressure-gradient strength and the maximum in the crossflow, and the dependence of the latter on distance from the surface was used to test analytical crossflow predictions. The data are in general agreement with Van Den Berg's law of the wall. The data also support the so-called parabolic law following a relaxation distance, especially if inviscid gradients are accounted for, and if the normal coordinate is contracted by the compressibility transformation.