The deformation microstructure and deformation process of the Mg-based long period stacking ordered (LPSO) phase accompanied by the formation of deformation kink bands were examined through dynamical observations during compression tests, and the features were compared to those in Zn single crystals. In both crystals, the formation of deformation kink bands was confirmed in specimens compressed along the direction parallel to the basal plane. The deformation kink bands formed in the directionally solidified (DS) LPSO phase crystals and the Zn single crystals had similar morphologies. Their formation induced plastic strain almost along the c-axis. However, their formation behaviors showed some different features. In the LPSO phase DS crystal, two different migration behaviors of the deformation kink band boundaries existed. The slower migration process was comparable to that observed in Zn single crystals. However, a migration process more than 105 times faster than the slower process was also monitored. The results imply that two different formation mechanisms of the deformation kink band might exist in the LPSO phase crystal.