The first detailed study of molecular ozone adsorption by means of FT-IR spectroscopy at low temperatures (77 K) is reported. The spectra of ¹⁶O₃, ¹⁸O₃ and mixed isotopic modifications adsorbed on silica and titania were observed. Ozone molecules reveal basic properties, forming hydrogen bonds with acidic surface OH groups via one of the terminal oxygen atoms. Fundamental frequencies of hydrogen-bonded ozone, calculated from the combination bands or measured directly, are close to those of physisorbed, liquid or dissolved molecules. Ozone adsorption on a titania surface dehydrated at different temperatures, or pre-exposed to pyridine, acetonitrile, CO₂ and CO, illustrates its interaction with Lewis acid sites of different strength. With weaker sites, ozone molecules form a coordination complex bound via one of the terminal oxygen atoms. The observed frequency values (about 1145 and 990 cm^-1), as well as isotopic shifts observed for ozone enriched with ¹⁸O, reveal a strong distortion of this molecule in the complex. The same form of ozone adsorption was found also for ZrO₂, MgO and CeO₂. No molecular adsorption of ozone on strong Lewis sites of TiO₂, Al₂O₃ or ZnO was detected. The data obtained provide evidence for ozone dissociation on these sites, resulting in the formation of atomic oxygen, which participate in the catalytic reactions of ozone decomposition or oxidation of CO on the oxide surfaces.