The adaptive character of crystal structure and microstructure of the modulated Ni-Mn-Ga and Ni-Mn-Sn phases was studied using synchrotron radiation and scanning electron microscopy (SEM) equipped with electron back scatter diffraction (EBSD). In-situ cooling/heating experiments have shown a significant difference in martensitic phase front propagation depending on the system investigated. Typical diamond like interfacial microstructures for alloys exhibiting higher twinning stresses was revealed. On the other hand, a planar phase front movement in single crystals with much lower twinning stresses was observed. Applying the complete crystallographic data the role of modulation and inverting staking faults (also refer to a/b boundaries) in self-accommodation process was investigated. To determine the real structure of modulated phases and confirm or exclude the adaptive concept the real single variant state of 14M and 10M martensite is studied.