<p>The recovery of nuclear magnetization after inversion was observed for the ⁶⁹Ga, ⁷¹Ga, and ⁷⁵As isotopes in chromium- and copper-doped semi-insulator GaAs crystals under continuous magnetic saturation of their spin-systems in comparison to the data for the undoped crystal. Different channels of nuclear spin-lattice relaxation were separated within a temperature range from 50 to 300&#xa0;K. The contribution to relaxation due to modulation of the crystalline electric field gradients on nuclei by thermal phonons, which is inherent for quadrupole nuclei, was found for all the crystals. However, it was comparable to the contribution to relaxation caused by paramagnetic centers and spin diffusion. Relaxation driven by electron centers was shown to be of the quadrupole nature for gallium isotopes, while the magnetic superhyperfine coupling became noticeable for ⁷⁵As nuclei below 100&#xa0;K. Doping GaAs with copper and chromium did not affect the rate of spin-lattice relaxation of the gallium and arsenic isotopes within the experimental accuracy. It was suggested that the EL2 centers play the major role in spin-lattice relaxation of the ⁶⁹&#xa0;Ga, ⁷¹&#xa0;Ga and ⁷⁵As nuclei via electron centers and spin diffusion.</p>