The dynamics of the Earth's deep interior are controlled to a large extent by rheological properties(1,2). Until recently, however, experimental studies on the rheological properties of materials thought to be present in the Earth's deep interior have been limited to relatively low pressures. Most previous estimates of rheology have therefore been based on either large extrapolations of low-pressure experimental data(3,4) or inferences from geodynamical observations(5-7). Such studies have provided only weak constraints on the complicated rheological structure expected in the transition zone of the Earth's mantle (between 410 and 660 km depth) where a series of phase transformations occur in silicate minerals(8). Here we report the results of a direct experimental study of deformation, under transition-zone conditions, of the spinel phase of (Mg,Fe)(2)SiO4 (ringwoodite; thought to be present in the Earth's transition zone). Relatively coarse-grained samples show evidence of dislocation creep with dislocation structures similar to those observed in oxide and germanate spinels(9,10), which have significantly higher creep strengths than olivine(10,11). In contrast, a fine-grained sample shows evidence for grain-size-sensitive creep. These observations suggest that a ringwoodite-rich layer of the transition zone is likely to have a higher viscosity than the olivine-rich upper mantle(3), whereas a subducting slab in the deep transition zone may lose its strength if significant grain-size reduction occurs(12-14).