High-temperature creep in single crystals of Y3Al5O12 (YAG) was studied by constant strain-rate compression tests. The creep resistance of YAG is very high : a stress of approximately 300 MPa is needed to deform at a strain rate of 10(-6) (s-1) at a temperature as high as 1900 K (approximately 0.84 T(m), (melting temperature)). YAG deforms using the [111] {11BAR0} slip systems following a power law with stress exponent n approximately 3 and activation energy E* approximately 720 kJ mol-1. However, a small dependence of n on temperature and of E* on stress was observed. This stress-dependence of activation energy combined with the observed dislocation microstructures suggests that the high creep resistance of YAG is due to the difficulty of dislocation glide as opposed to the difficulty of climb. Present dislocation creep data are compared with diffusion creep data and a deformation mechanism map is constructed. Large transition stresses (2-3 GPa for 10 mum grain size) are predicted. Implying that deformation of most fine-grained YAG will occur by diffusion creep.