Using X-ray absorption spectroscopy we have investigated the local structure of Yb2O3 and Lu2O3 thin films deposited on Si(1 0 0) by means of atomic layer deposition. These two oxides, as well as those of the other rare earth elements, are considered among the high dielectric constant materials candidates to substitute SiO2 in ultra-scaled CMOS devices. We find that the films maintain the overall bixbyite structure of the bulk oxides, but exhibit significant distortions of the local structure depending on thickness and thermal treatment.