Samples of CdTe single crystals which are used as radiation detectors were periodically measured during a long time interval with different values of an applied voltage. The samples were also periodically exposed during long time periods to high temperatures of 390 K and to rapid changes of temperature from 300 K to 390 K. After 1.5 years of measurements we observed ageing of the samples which resulted in deterioration of their transport characteristics. The resistance of the samples increased significantly and current-voltage characteristics were unstable in time. Noise spectroscopy showed that low frequency noise can be used for detection of CdTe sample ageing as its spectral density increases significantly comparing to the 1/f noise of a high quality sample