Dislocation mobilities in quasicrystals are calculated from recently developed hydrodynamic equations. The mobilities are expressed in terms of vacancy diffusion constants for the quasicrystal. Estimates of these diffusion constants based on their values in conventional crystals lead to far smaller dislocation mobilities than in conventional crystals. Plastic flow should therefore be effectively prohibited; one dramatic consequence is that quasicrystals should be extremely brittle. A detailed microscopic calculation of vacancy diffusion constants is urged. Implications for icosahedral-order theories of glasses are discussed. © 1986 The American Physical Society.