The steady-state flow properties of the continental lithosphere play an important role in a wide range of geological processes(1). A complete dynamic description of lithospheric deformation requires information about the magnitude of driving forces and the rheology of the crust and lithospheric mantle, about which there is little agreement(2-6). Here we constrain these properties by analysing variations in strain rate during the extension of continental lithosphere. We determine the temporal variation of strain rate from the subsidence curves of a global sample of Phanerozoic sedimentary basins. The peak strain rate and final strain estimated from these strain-rate histories suggest that the cessation of extension is governed by cooling and concomitant strengthening of the underlying lithospheric mantle. Dynamic modelling of these data indicates that the rheology of the lithosphere is controlled by power-law creep with a stress exponent of three and an activation energy of similar to 500 kJ mol(-1). This rheology is consistent with that inferred from laboratory experiments on dry olivine(7) extrapolated to lithospheric conditions.