Inhomogeneous deformation behavior in a magnesium alloy which is almost occupied by long-period stacking order (LPSO) phase has been investigated by using high-precision marker method and SEM observation. Particular emphasis is laid on the aspect of kinks, which is one of the characteristic microstructures generated in the LPSO phase. Mg alloys containing some transition metals such as Zn and rare earth elements such as Y or Gd have a characteristic microstructure including the LPSO phase and the usual hcp matrix phase. The superior mechanical properties of the Mg alloy should be closely related not only to the microstructural inhomogeneity induced by the difference in the deformability of the dual phases but also to the characteristic deformation microstructures of LPSO phase. The kinks were generated by working such as extrusion in the LPSO phase, which raises the strength of LPSO phase. Then, such hard LPSO phase should contribute to the increase of yield and tensile strength of the alloy. SEM-EBSD analysis revealed the many wedge-shape microstructures with high angle boundaries, which indicates that the kinking occurred by the compression test. In order to clarify the details of such kinking behavior, high-precision marking method using electron beam lithography has been employed. Large distortion of markers and migration of kink wall were observed on the specimen surface. The formation mechanism of such microstructural inhomogeneity in the LPSO phase is discussed.