Laser induced picosecond transient gratings are used to study carrier transport via free carrier and photorefractive nonlinearities. Carrier lifetime (tau(R) = 1.7 ns), hole and ambipolar mobilities (mu(h) = 85 cm2 V-1 s-1 and mu(a) = 146 cm2 V-1 s-1) are measured directly, and electron mobility equal to 520 cm2 V-1 s-1 is calculated for CdTe:V at an impurity concentration of 10(19) cm-3. Feed-back effect of light induced space charge electric field is found responsible for diffracted beam intensity modulation during the grating recording and its decay.