The melt-spun (MS) Ti50Ni25Cu25 alloy and the Zr62Cu22A110Fe5Dy1 bulk metallic glass (BMG) were subjected to high pressure torsion (HPT). X-ray diffraction (XRD) measurements show a shift of the first diffraction halo to a low angle after HPT processing, which corresponds to an increase in the values of the radius of the first coordination sphere and the free volume. Direct density measurements confirmed an increase in free volume values. A special TEM procedure was used for a detailed study of the microstructure of both amorphous alloys after HPT processing. The study revealed the formation of a large density of shear bands (SBs) in both alloys. Nanocrystals are formed directly in shear bands as a result of strain-inducted nanocrystallization. Amorphous nanoclusters with a size of 20 nm are formed in an amorphous matrix surrounding the SBs in the HPT-processed MS alloy Ti50Ni25Cu25. The formation of nanoclusters was not observed in BMG Zr62Cu22A110Fe5Dy1 after HPT processing.