The elastic displacement field around a uniformly moving edge dislocation has been obtained for the case where the dislocation glides on a (111) plane in a ⟨110⟩ direction in an anisotropic face‐centered‐cubic crystal. An equation is obtained for the velocity (the Rayleigh wave velocity) at which the shear stress on the slip plane of a moving dislocation is zero. Dislocations of like sign moving at velocities faster than this velocity attract rather than repel each other. It is concluded that when anisotropy is small and the elastic constantc11is smaller thanc12+2c44(the more commonly occurring relationship between the elastic constants) the Rayleigh wave velocity is increased above its value in an isotropic crystal and therefore, the extent of the velocity region where dislocations exhibit an anomalous behavior is decreased. For slightly anisotropic crystals the limiting velocity of dislocation motion is the slower of the two shear velocities in the ⟨110⟩ direction.