Molecular-dynamics methods have been employed to investigate atomic displacement mechanisms in Ni50Zr50 metallic glasses both in the absence and in the presence of an elastic shear stress. Calculations were performed on systems subjected to a different number of hydrostatic compression cycles. In all the cases, local collective rearrangements of Ni and Zr atoms connected in clusters are observed. Numerical findings indicate that rearrangements occurring in unstrained and strained systems involve roughly the same regions. In addition, compression cycles produce the same effects on atomic mobility in unstrained and strained systems. This suggests the existence of regions characterized by a particular structural instability that determines a significant correlation of atomic displacements in unstrained and strained systems.