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Carrier drift mobilities of CdZnTe (CZT) grown by the high-pressure Bridgman (HPB) method and chlorine-doped CdTe grown by the traveling heater method (THM) were measured by a time-of-flight (TOF) technique. A spectrometer-grade crystal of HPB CZT shows room-temperature electron mobility of 960 cm2/Vs and hole mobility of 56 cm2/Vs. Both electron and hole mobility of THM CdTe:Cl crystals are higher (1100 cm2/Vs for electrons and 88 cm2/Vs for holes) than that of the HPB CZT crystal. Both materials show a saturation of the electron mobility at low temperature around 100 K and a strong decrease of the hole mobility with a lowering of the temperature. Theoretical mobility has been calculated by solving a Boltzmann transport equation assuming several scattering mechanisms such as polar optical phonon, ionized impurity, and alloy scattering. It is concluded from the comparison of the experimental and theoretical temperature dependence that shallow trap-controlled mobilities are observed in both spectrometer-grade CdZnTe and CdTe crystals.