Two non-first-order kinetic peaks at about 350 and 500 K appear in the thermoluminescence (TL) spectra of single-crystal and polycrystalline ${\mathrm{MgAl}}_{2}$${\mathrm{O}}_{4}$ irradiated with ionizing radiation at room temperature. Among others, emission from ${\mathrm{Cr}}^{3+}$ and ${\mathrm{Mn}}^{2+}$ ions are observed. TL measurements at different wavelengths indicate that the emitting centers have different recombination probabilities. Thermally-stimulated-current and thermoelectric-power measurements, together with results on the TL excitation spectra with ultraviolet radiation, indicate that both processes are due to thermally released electrons from traps. The V centers also act as recombination centers leading to a complex emission band at around 4.9 eV. Experimental results and numerical simulations based on a recently proposed mathematical model suggest that the massive presence of lattice defects, as a result of the antisite disorder and the nonstoichiometry of synthetic spinel crystals, may have a strong influence on electron-trapping and -detrapping processes, leading to complex-kinetics TL phenomena.