The electronic and magnetic states, chemical bonding and reactions, and phonon spectrum of the plutonium hydrides Puliz (x = 2, 3) are investigated by employing first-principles calculations by means of the density functional theory (DFT) + U approach. The strong correlation and the spin-orbit coupling (sac) effects on these 5f electrons systems are systematically studied. Results show that both the strong correlation and the SOC play critical roles in correctly describing their ground-state properties. The antiferromagnetic configuration of PuH2 is found energetically most stable while for PuH3 the ferromagnetic state is the most stable state. Our calculated phonon spectra clearly indicate the dynamical stability of these magnetic configurations. For PuH3, more electrons from the Pu atoms are released to bond with H than that in PuH2. As a result, the lattice constant is contracted by increasing the H concentration. Reacting from metal Pu and molecule H-2, more PuH3 should be produced than PuH2 in low temperature condition. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.