The regularities in the inhomogeneous development of plastic deformation at the front of the Lüders band at the yield plateau in Hadfield steel single crystals are considered. It has been established that the Lüders front moves in jumps under these conditions. This character of motion is associated with the rearrangement of the inhomogeneous distributions of the components of the plastic distortion tensor components at the deformation front. A plausible estimate of the frequency of oscillations in the development of the Lüders front has been obtained.