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We examine the frequency dependence of the energy relaxation of hot electrons under the influence of an intense oscillating electric field of terahertz frequency. The calculated energy-loss rates in a GaAs/AlGaAs heterojunction and two GaAs-based quantum wells exhibit a frequency behavior quite different from that of the widely used Kogan formula. Their ratio shows an unexpected peak at around 0.5–0.6 THz, with a height about 3–10 times of its low-frequency value. This remarkable resonance is a unique indication of the role of the Doppler shift of the phonon frequency. © 1998 American Institute of Physics.