Reactions of laser ablated cerium atoms with hydrogen peroxide or hydrogen and oxygen mixtures diluted in argon and condensed at 4 K produced the Ce(OH)(3) and Ce(OH)(2) molecules and Ce(OH)(2)(+) cation as major products. Additional minor products were identified as the Ce(OH)(4), HCeO, and OCeOH molecules. These new species were identified from their matrix infrared spectra with D2O2, Dy and O-18(2) isotopic substitution and correlating observed frequencies with values calculated by density functional theory. We find that the amounts of Ce(OH)(3) and of the Ce(OH)(2)(+) cation increase on UV (lambda > 220 nm) photolysis, while Ce(OH)(2), Ce(OH)(4), and HCeO are photosensitive. The observed major species for Ce are in the +III or +II oxidation state, and the minor product, Ce(OH)4, is in the +IV oxidation state. The calculations for the vibrational frequencies with the B3LYP functional agree well with the experiment. The NBO analysis shows significant backbonding to the metal 4f and Sd orbitals for the closed shell species. Most open shell species have the excess spin in the 4f with paired spin in the Sd due to backbonding. The heats of formation of the observed species were derived from the available data from experiment and the calculated reaction energies. The major products in this study are different from similar reactions for Th where the tetrahydroxide was the major species.