Transversely homogeneous, uniformly sheared, turbulent flow was allowed to reach its asymptotic structure in a straight wind tunnel section and then it was passed through a sequence of two curved sections and a final straight section. The cross-sectional shape of the entire wind tunnel was rectangular, while the two curved sections had circular centrelines with the same radius but opposing curvatures. In all cases, the mean strain rate due to curvature was relatively weak (±5%), compared to the mean shear rate, but its effects on the turbulence kinetic energy and structure were substantial; streamwise pressure gradient effects were negligible. The turbulence structure approached approximately self-similar states towards the downstream ends of each curved section but the main interest of the present study was the rate of adjustment of the turbulence following a stepwise change in curvature. It has been shown that the adjustment of the shear stress anisotropy, which is a sensitive indicator of structural changes, can be approximated by a first-order system response, whose time constant scales with the inverse mean shear and is independent of the curvature parameter. Uniformly sheared flow results were used for an interpretation of the structure of curved turbulent boundary layers, both during adjustment and in a fully developed state.