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Transient-current technique was used for measuring the profile of the electric field in CdTe and CdZnTe samples excited by an 241Am α-particle source. Current waveforms were analyzed by a general model, which involved both the effect of the space charge in the depleted region and charge trapping. The carrier mobility and the electric-field profile were also evaluated in this way. The maximum electric field was observed close to the cathode, whereas the minimum occurred near the anode. The decrease in the strength of the electric field from cathode to anode was explained in terms of a positive space charge formed in the detector's volume. Measurements under incomplete depletion, when an “inactive” region with zero electric field was observed under the anode, were reported as well. Space-charge densities of 1011-1012 cm-3 in CdTe and 1010 cm-3 in CdZnTe were evaluated. The dynamics of electron-hole plasma formed by a single α-particle absorption event was analyzed in detail and used as a complementary test of our reported model. An excellent agreement with theory was obtained.