The present work attempts to study tentative gamma dose rate effects for the stable TL and OSL signals of specific, well established artficial luminescence dosimeters. Two different dose rates of gamma radiation (2 and 31 Gy/h) were used. The study has been performed to the stable TL peaks of 5 different TL phosphors (LiB4O7:Cu,In; MgB4O7:Dy,Na; LiF:Mg,Ti; CaF2:Dy; BeO) as well as to both OSL components of BeO. Tentative dose rate effects were studied for both dosimetric dose response features as well as kinetic parameters after deconvolution for both signals. Two different groups of materials were revealed. The first one includes materials such as LiF: Mg,Ti, BeO and MgB4O7: Dy,Na; for these, both TL dose response features and TL kinetic parameters are independent on the dose rate. This is also the case for both OSL components of BeO besides the linearity index of the dose response of the fast OSL component; the latter seems to mildly depend on the dose rate. At the same time, experimental arguments based on both dosimetric as well as deconvolution features suggest the presence of tentative dose rate effects for the cases of LiB4O7:Cu, In and CaF2:Dy. Moreover, the effective use of these aforementioned features as probes for identification of dose rate effects is also discussed. The results of the present study suggest that the basic postulate of most phenomenological TL models that traps pre-exist and they are simply filled during irradiation has to be reconsidered.