Hydrogen adsorption on the (10 (1) over bar 0) surfaces of Ru and Re leads to the formation of c(2x2)-3H phases. As determined by quantitative low-energy electron diffraction (LEED) and density functional theory calculations, hydrogen atoms, as expected, occupy threefold coordinated hcp sites along the densely packed rows and the unexpected short-bridge sites along the ridges in both c(2x2) phases. The Ru and Re substrates reconstruct only weakly and in a very similar fashion under hydrogen chemisorption. Most notably, there is a buckling in the third substrate layer of about 0.06 Angstrom. Probably (though not outside the limits of error), there are also slightly lateral displacements (0.02 Angstrom) of top-layer substrate atoms which are bridge-coordinated to hydrogen. The metal-hydrogen bond lengths determined for both surfaces correspond to hydrogen radii in the expected range of 0.4-0.7 Angstrom.