An optical-pumping technique is used to measure the spin-relaxation time of photogenerated conduction electrons in several p-type GaAs single crystals doped with various amounts of acceptors in the 1.7-300 K temperature range. Our experimental results are compared with those of the literature and with the predictions of the existing theoretical calculations. From about 10 K, the Sir-Aronov-Pikus {BAP) mechanism is found to be relevant for moderately doped (10"-10" cm '}, up to about 150 K, or degenerate (up to 300 K) semiconductors, using the electronic temperature, deduced from the luminescence spectra, rather than the sample temperature. The D'yakonov-Perel' (DP} process was found to be active above 200 K for moderately doped samples and from about 80 K to room temperature for samples doped in the (1.6-6))&10' -cm ' acceptor-concentration range. Our original results obtained at liquid-helium temperatures at whatever the doping level cannot be explained either by the DP mechanism or by the BAP process.