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Physical processes (e.g. solid-state creep and electrical conduction) as well as chemical kinetics are determined by diffusion rates in minerals. However, diffusion coefficients in high-pressure phases of the Earth´s mantle (e.g. wadsleyite, ringwoodite and silicate perovskites) have not been determined because of experimental difficulties. Due to the availability of relatively large (~ 300 µm) crystals and a specially-designed gold sample capsule, we have been able to measure Fe-Mg diffusion rates and the activation energy for this process in (Mg,Fe)₂SiO₄ wadsleyite in a compositional range (X_Mg = 0.9-0.8) relevant to the Earth´s mantle. We used diffusion couples consisting of (1) a single crystal and (2) coarse-grained polycrystalline wadsleyite to perform diffusion anneals at 1100-1300°C at 15 GPa for durations ranging from 1.5-24 hours in a multi-anvil apparatus. For comparison, similar experiments were also performed on olivine at 1400°C and 9-12 GPa. Diffusion coefficients obtained by fitting the resulting concentration profiles are about two orders of magnitude larger for wadsleyite (e.g. 5 x 10^-15 m² s^-1 at 1200°C) than for olivine (based on an extrapolation of the olivine data). This implies that rates of chemical mixing will be enhanced in the mantle transition zone, in spite of the increase in pressure, which usually inhibits rates of diffusion. It should be possible to use our experimental approach to perform similar experiments at pressures up to 25 GPa, which thereby opens the possibility of obtaining diffusion data in all major high-pressure mantle phases for the first time.