We investigated the initial stage of the oxidation of H-terminated Si (100) and (111) surfaces in oxidation solution. A specially designed spectrochemical cell in attenuated-total-reflection geometry was used for observing infrared absorption feature attributed to these surfaces in a contact with the solution. After removing surface oxide and making an H-terminated surface by HF solution, we introduced the oxidation solution into the cell and recorded infrared spectra as a function of time, after exchanging the solution to deionized water to pose the oxidation. We used 3% of H₂O₂ and 2 ppm of ozonized water as the oxidation solutions. We found that the time evolution of the surface hydride structures, which were observed from 2000 to 2300 cm^-1, appeared differently, depending on both the surface orientation and the oxidation solution. With either H₂O₂ solution or ozonized water, we observed one of the oxide structures of -O₃SiH but the other oxide structures such as - (O₂Si) SiH and - (OSi2) SiH were not observed on Si (100) as oxide intermediates. On the other hand, all the intermediate structures were observed on (111). When we continued the oxidation for 10 min in ozonized water, all hydride structures were disappeared on both (100) and (111), while a part of the hydride structures were still observable in H₂O₂ solution. We discussed these features on a basis of our in-situ experiment.