X-ray luminescence (XL), thermally and optically stimulated luminescence (TL and OSL) of the Er 0,05Dy 0,05Y 2,9Al 5O 12 crystals are investigated in comparison with an anion-defective corundum and corundum-based TLD-500K detectors. It is shown that the TL curves of the (Er 3+, Dy 3+):YAG samples measured within a wide spectrum range from 200 to 800 nm have a simple shape with a single peak centered at 170 °С, the thermal activation processes of which can be very well described in terms of monomolecular kinetics. The TL response of YAG varies linearly within the 10-10 4 mGy range. Continuous wave optically stimulated luminescence (CW-OSL) decay curves are studied using white and blue (470 nm) LEDs. White LED is more advantageous as compared to blue LED due to reduction of measuring time, increase of the OSL yield and initial intensity. By a comparative study of the TL, OSL and dose-response dependences of the (Er 3+, Dy 3+):YAG crystals with TLD-500K detectors it is shown that the YAG samples doped with REelements can be considered to be as promising TL- and OSL-dosimetry materials. It is ascertained that the TL and OSL responses of the YAG samples with the given concentration of the Er 3+ and Dy 3+ ions are two orders of magnitude lower than TLD-500K detectors.