We demonstrate that a parametrically pumped picosecond laser has enough coherence and energy to write transient phase gratings at nonresonant interaction, thus allowing a study of time-resolved carrier transport in CdTe crystals to be made. Autocorrelation trace of light diffraction efficiency on transient grating allowed us to measure a coherence length of the parametric generator. Carrier diffusion, recombination, and drift in light-created internal space-charge ~SC! electric fields have been studied in vanadium or germanium doped semi-insulating CdTe crystals by nonresonant four-wave mixing technique at 940 nm wavelength. It was found that modification of the deep level charge state in CdTe:V by As codoping has changed the sign of majority carriers, responsible for the creation of SC field. Dynamics of free carrier grating decay in CdTe:Ge revealed an electron-governed very fast initial grating decay which develops with time into the double-exponential hole-governed grating decay. Time-resolved transient grating technique described in this article provides a powerful tool for investigation of the role of deep traps in photorefractive semiconductors and optimization of their photoelectric properties in a required temporal and spectral range