Circularly polarized light is emitted in radiative transitions of polarized electrons from the conduction to the valence band in GaAs or GaAs1-xPx crystals. The degree of light polarization is directly related to the polarization of the conduction-band electrons at the instant of recombination and allows conclusions about the depolarization of electrons in the conduction band. The depolarization is caused by spin-relaxation processes. The efficiency of these processes depends on crystal type, crystal temperature, degree of doping, and kinetic energy of the electrons. Highly p-doped GaAs and GaAs0.62P0.38 crystals (NA>1×10^19 atoms/cm^3) were bombarded with polarized electrons (initial polarization 38 %), and the spectral distribution and the circular polarization of the emitted recombination radiation were measured. The initial kinetic energy of the electrons in the conduction band was varied between 5 and 1000 eV. The measurements of the spectral distribution show that the electrons are thermalized before recombination occurs, independent of their initial energy. An important thermalization process in this energy range is the excitation of crystal electrons by electron-hole pair creation. The circular polarization of the recombination radiation lies below 1% in the whole energy range. It decreases with increasing electron energy but is still of measurable magnitude at 100 eV in the case of GaAs0.62P0.38. The circular polarization is smaller for GaAs than for GaAs0.62P0.38, which we attribute to more efficient spin relaxation in GaAs.