The time dynamics of nonequilibrium charge carrier relaxation processes in SI GaAs:EL2 (semi-insulating gallium arsenide compensated with EL2 centers) and HR GaAs:Cr (high-resistive gallium arsenide compensated with chromium) were studied by the optical pump–terahertz probe technique. Charge carrier lifetimes and contributions from various recombination mechanisms were determined at different injection levels using the model, which takes into account the influence of surface and volume Shockley–Read–Hall (SRH) recombination, interband radiative transitions and interband and trap-assisted Auger recombination. It was found that, in most cases for HR GaAs:Cr and SI GaAs:EL2, Auger recombination mechanisms make the largest contribution to the recombination rate of nonequilibrium charge carriers at injection levels above ~(0.5–3)·1018 cm−3, typical of pump–probe experiments. At a lower photogenerated charge carrier concentration, the SRH recombination prevails. The derived charge carrier lifetimes, due to the SRH recombination, are approximately 1.5 and 25 ns in HR GaAs:Cr and SI GaAs:EL2, respectively. These values are closer to but still lower than the values determined by photoluminescence decay or charge collection efficiency measurements at low injection levels. The obtained results indicate the importance of a proper experimental data analysis when applying terahertz time-resolved spectroscopy to the determination of charge carrier lifetimes in semiconductor crystals intended for the fabrication of devices working at lower injection levels than those at measurements by the optical pump–terahertz probe technique. It was found that the charge carrier lifetime in HR GaAs:Cr is lower than that in SI GaAs:EL2 at injection levels > 1016 cm−3.