We study IR absorption spectra of various isotopomers of the HXeOH molecules isolated in solid Xe at 7 K. Upon the O-16 to O-18 isotopic substitution, we found experimentally an anomalous shift of the H-Xe stretching vibration frequency of HXeOD and HXeOH. This spectral behavior, when the fundamental frequency shifts up in energy for the heavier oxygen isotope, cannot be understood on the basis of the harmonic approximation for fundamental vibrations, and the anharmonic coupling between normal modes is presumably responsible for this anomalous effect. Our anharmonic CC-VSCF calculations describe correctly the experimental observations.