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The authors present a theory of dc photoresponse in two-dimensional (2D) electron channel in the grating-gated field-effect transistor irradiated by an electromagnetic wave of terahertz frequency. The authors determine photoinduced dc correction to the source-drain voltage and demonstrate that it has resonant peaks when the frequency of an external radiation coincides with 2D plasmon frequencies. The photoresponse is shown to depend on the asymmetric electron drag in the 2D channel with constant bias current. The amplitude of the resonant peaks has nonmonotonic temperature dependence with a maximum at elevated temperatures. The results explain qualitatively some important features of the photoresponse observed in recent experiments.