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High resistivity (108-109 Ωcm) CdTe samples (undoped, Cl and In doped) were investigated by means of spectral and temperature dependent photoconductivity (PC) with the goal to look for correlations of the signal from deep levels and transport properties represented by the mobility-lifetime product. For comparison, low temperature PC measurements were performed on p-type undoped CdTe crystals having a low resistivity at room temperature. It was found out, that the transition dominating the below bandgap PC in these undoped samples has the energy EV+0.95 eV. We suppose, that the corresponding defect is native, probably related to Cd vacancy or Cd vacancy complex. Doping with shallow donors (In,Cl) results in practical disappearance of this transition. The near midgap PC signal is observed in high resistivity undoped CdTe, although with lower intensity, than in case of low resistivity p-type undoped samples. A correlation between intensity of the EV+0.95 eV PC transition and the mobility lifetime measured by alpha spectroscopy was observed. We suppose, that this deep level acts as a significant trap influencing performance of X and gamma ray detectors. Doping with shallow donors probably results in physical removing of the corresponding defect by a reaction with InCd or ClTe shallow donors, significantly reducing its ability to trap electrons.