In this communication we report on the application of low temperature thermoluminescence (ltTL) associated with shallow traps in the research on scintillation properties of cerium doped LuAP and YAP crystals. We show that existence of shallow traps and their interference with the scintillation process readily explain changes in light yield and time profiles with temperature. The analysis of two major glow peaks at 183 and 270 K of LuAP:Ce yields trap parameters: The activation energy E=0.507 eV; the frequency factor s=3.65×1012 s−1 and E=0.786 eV; s=1.77×1013 s−1, respectively. A glow curve of YAP:Ce also shows two major glow peaks at 108 K and 154 K, although this case is more complex and involves a distribution in the energies. Assuming a Gaussian distribution with the standard deviation σ≅0.018 eV we find trap parameters to be: E=0.30 eV (the mean); s=5×1012 s−1 and E=0.5 eV; s=7×1014 s−1, respectively. Then using the obtained trap parameters we calculate examples of time profiles and light yield characteristics to compare them to the experimental results.