The localized plastic flow auto-waves observed for the stages of easy glide and linear work hardening in a number of metals are considered. The propagation rates were determined experimentally for the auto-waves in question with the aid of focused-image holography. The dispersion relation of quadratic form derived for localized plastic flow auto-waves and the dependencies of phase and group rates on wave number are discussed. A detailed comparison of the quantitative characteristics of phase and group waves has revealed that the two types of wave observed for the stages of easy glide and linear work hardening are closely related. An invariant is introduced for localized plastic flow phenomena occurring on the micro- and macro-scale levels in the deforming solid.