To study the fluxionality of the bis(dihydrogen) complex RuH2(H2)2(PCy3)2 (1), NMR spectra were recorded in Freons (mixture of CDCl3, CDFCl2, and CDF2Cl). 1 was found to remain fluxional at all temperatures, but the presence of CDCl3 necessary for its solubilization induces its transformation into, first, RuHCl(H2)2(PCy3)2 (3) and the new ruthenium(IV) dihydride RuH2Cl2(PCy3)2 (4). 4 is produced selectively in pure CDCl3 but reacts further to give a mixture of chloro complexes. 4 was isolated from the reaction of 1 with aqueous HCl in Et2O and shows a fluxional process attributed to the interconversion between two symmetrical isomers. The activation parameters of this process were obtained by 1H NMR line shape analysis, as well as those corresponding to the exchange between 3 and free dihydrogen. The fluxionality of the dihydrogen - hydride system is also evident at a much faster time scale than that of NMR studies in the inelastic neutron scattering observations of the rotation of the dihydrogen ligands. The geometries and relative energies of several isomers of complexes 1, 3, and 4 were studied using density functional theory (DFT) and MP2 methods, together with a few coupled-cluster (CCSD-(T)) calculations. In contrast to what might have been expected, the two hydrides and the two H2 units of 1 lie in the same plane, due to the attractive "cis effect" created by the hydrides. The two H2 ligands adopt cis positions in the lowest-energy isomer. Rotation of the two dihydrogen ligands has been analyzed using DFT calculations. A slight preference for a C2 conrotatory pathway has been found with a calculated barrier in good agreement with the experimental INS value. Two low-energy isomers of 4 have been characterized computationally, both of which have C2u symmetry, consistent with the solution NMR spectra.