We measured timing properties of CdTe and CdZnTe semiconductor detectors with planar configuration. We developed a new method to evaluate their performance in timing resolution utilizing an 241 Am doped plastic scintillator. We confirmed that the low mobility and short life time of holes are major obstacles to their timing resolution. However, their timing properties can be very much improved, either by applying a high electric field that increases the carrier speed, or by selecting those events which are dominated by the electron signal. We demonstrated the latter, through a pulse-shape discrimination technique using two different integration time constants. In conjunction with a newly developed CdTe diode, we obtained a superior timing resolution of 5.8 nsec. We also discussed the application of CdTe to Positron Emission Tomography, employing the standard 511 keV gamma-gamma coincidence method. We confirmed that a geometrical configuration in which the electrodes are parallel to the incident γ-rays gives about 3 time better timing response than a geometry when the electrodes are perpendicular to the γ-ray beam.