Proton-bound rare-gas dimer (RgHRg)(+), in which Rg represents a rare-gas atom, serves as a prototypical system for proton solvation by inert-gas atoms. Until now, only centrosymmetric species with Rg = Ar, Kr, or Xe have been identified with infrared spectra. We employed electron bombardment during deposition of a mixture of Xe (or Kr) in p-H-2 at 3.2 K to prepare (RgHRg)(+). Lines at 847.0 and 972.1 cm(-1) are assigned as the Rg-H-Rg antisymmetric stretching (nu(3)) mode and its combination with the RgHRg symmetric stretching (nu(1) + nu(3)) mode of (XeHXe)(+) in solid p-H-2, respectively. Lines at 871.1 and 974.0 cm(-1) are assigned as the nu(3) and nu(1) + nu(3) modes of (KrHKr)(+) in solid p-H-2, respectively. Slightly shifted and broadened lines were observed for these species in solid n-H-2. These results agree satisfactorily with reported experimental values of (XeHXe)(+) and (KrHKr)(+) in solid Xe, Kr, and Ar, and with the quantum-chemically predicted anharmonic vibrational wavenumbers of these species in the gaseous phase; the significant spectral shifts in various matrixes are rationalized with the proton affinities of the hosts. When a mixture of Xe and Kr in p-H-2 was used, an additional broad feature at 1284 cm(-1) was observed and assigned as the nu(3) mode of (KrHXe)(+) in solid p-H-2. This line shifted to 1280 cm(-1) in solid n-H-2 and the corresponding line of (KrDXe)(+) was observed at 954 cm(-1) in n-D-2. The observations of these lines are new; the wavenumbers significantly blue shifted from those of the centrosymmetric (RgHRg)(+) agree with the quantum-chemically predicted anharmonic vibrational wavenumbers of 1279 cm(-1) for (KrHXe)(+) and 916 cm(-1) for (KrDXe)(+). Analysis of the computational results shows that electronic correlation effects play a much greater role for the asymmetric than for the symmetric species. An interpretation for this is provided.