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Luminescent properties of molybdates have been a subject of intensive research for last years. Some of the molybdates were shown to be prospective for use as cryogenic scintillating bolometers in the search of neutrinoless double beta decay [1]. A charge carrier trapping was observed in all the molybdates at low temperatures. Even shallow traps can be a reason for decrease scintillation efficiency under operating conditions and it is a serious problem for cryogenic scintillators. The origin of traps in molybdates is still not clear yet. In this paper we try to clarify the origin of traps in molybdates. SrMoO4, PbMoO4 and ZnMoO4 were chosen for the study. Thermostimulated luminescence (TSL) techniques and numeric modeling was implemented for the study. TSL curves and spectra were measured at the Laboratory PCML, Claude Bernard Lyon University. An X-ray source with a tungsten anode operating at U = 30 keV was used as an excitation source. Luminescence characteristics under excitation in UV and VUV spectral region have been measured at the SUPERLUMI station in the synchrotron radiation channel of the storage ring DORIS III (DESY, Hamburg) [2]. Numeric modeling was performed in computational software program Mathematica 7.0. SrMoO4 and PbMoO4 single crystals were grown by the conventional Czochralski method in a Pt crucible in air. Samples of ZnMoO4 were grown using low temperature gradient Czochralski technique that allows growing crystals with improved optical properties [3]. The concentrations of contaminating impurities were determined by atomic-emission spectral analysis. TSL curves were approximated as using the first order decay approximation consuming that the probability for a charge carrier released from traps to be captured by traps again is much lower than the probability of radiative recombination as well as using the second order decay approximation too (the opposite ratio of the probabilities). Frequency factors and activation energies of traps were obtained. Numeric modeling performed in system of kinetic equations allows to approximate experimental TSL curves and gives an estimation of traps concentration. We conclude that charge carriers are trapped by regular complexes MoO4. Self-trapped holes supposed to be observed in SrMoO4 and self-trapped electrons in PbMoO4. It is shown for the first time that both self-trapped electrons and holes exist in ZnMoO4. The financial support of RFBR 11-02-01506-а and BMBF Project RUS 10/037 grants is gratefully acknowledged.