First-principles calculation reveals that the spin-orbit coupling (SO) should have an important effect on lowering the total energy of each HfHx (x = 1, 1.25, 1.5, 1.75, and 2) phase with the FCC (delta) and FCT (gamma and epsilon) structures, while has a negligible effect on structural stability of various HfHx phases as well as atomic structure and lattice constants of FCC HfHx phases. Calculations also show that mechanical stability plays a more significant role than thermodynamics in determining the existence of various HfHx phases as well as phase transitions between delta, gamma, and epsilon. Moreover, the intrinsic composition range of the delta -> epsilon transition from the present study is 1.75 <= x <= 2, which could clarify the controversy of experimental observations in the literature. In addition, the splitting of degenerate bands and the change of density of states at Fermi level would bring about a deep understanding of the effect of SO on stability of various HfHx phases. (C) 2013 Elsevier B.V. All rights reserved.