The dissociation and formation of water on the Rh(111) and Ni(111) surfaces have been studied using density functional theory with generalized gradient approximation and ultrasoft pseudopotentials. Calculations have been performed on 2x2 surface unit cells, corresponding to coverages of 0.25 ML, with spot checks on 3x3 surface unit cells (0.11 ML). On both surfaces, the authors find that water adsorbs flat on top of a surface atom, with binding energies of 0.35 and 0.25 eV, respectively, on Rh(111) and Ni(111), and is free to rotate in the surface plane. Barriers of 0.92 and 0.89 eV have to be overcome to dissociate the molecule into OH and H on the Rh(111) and Ni(111) surfaces, respectively. Further barriers of 1.03 and 0.97 eV need to be overcome to dissociate OH into O and H. The barriers for the formation of the OH molecule from isolated adsorbed O and H are found to be 1.1 and 1.3 eV, and the barriers for the formation of the water molecule from isolated adsorbed OH and H are 0.82 and 1.05 eV on the two surfaces. These barriers are found to vary very little as coverage is changed from 0.25 to 0.11 ML. The authors have also studied the dissociation of OH in the presence of coadsorbed H or O. The presence of a coadsorbed H atom only weakly affects the energy barriers, but the effect of O is significant, changing the dissociation barrier from 1.03 to 1.37 and 1.15 eV at 0.25 or 0.11 ML coverage on the Rh(111) surface. Finally, the authors have studied the dissociation of water in the presence of one O atom on Rh(111), at 0.11 ML coverage, and the authors find a barrier of 0.56 eV to dissociate the molecule into OH+OH.