The theory of non-linear interaction of electromagnetic radiation with hybrid plasmonic structure, which consists of the two-dimensional quantum heterostructure integrated with a plasmonic element in the form of a metal grating, is developed. In particular, the non-linear effect of a detection of high-frequency radiation by a drifting two-dimensional electron gas is examined. Based on the self-consistent solutions of the Maxwell and non-linear hydrodynamic equations in the frames of consistent perturbation theory of the second order, the expression of a photoresponse in the THz region is found. It is shown that the obtained expression contains an additional factor corresponding to the radiative decay rate. The latter was omitted in the previous theories. The presented theory is applied to the analysis of high-frequency properties of hybrid plasmonic structures on the basis of AlGaAs/GaAs quantum heterostructure. The influences of an optically thick substrate and the effect of the electron heating under high electron drifts on the spectral characteristics of the transmission/absorption coefficients and on the photoresponse spectra are analyzed. Some recommendations as for the design of efficient terahertz radiation detectors with the use of the hybrid plasmonic structures as a core element are given. K e y w o r d s: THz plasmonics, THz detection, hybrid plasmonic structures.