We show a mechanism for angle-dependent resonant oscillations of high-frequency conductivity and surface impedance in organic Q2D conductors in the presence of strong magnetic field H_0. In highly anisotropic conducting systems, the drift velocity vD of electrons is an oscillatory function of the angle of the magnetic field direction. As a result the location of Landau absorption regions depends on the orientation of H_0. Under the condition of anomalous skin effect, when the displacement of an electron over the period of electron motion in a magnetic field exceeds skin depth, the Landau damping becomes essential. In this case the angle-dependent oscillations of high-frequency conductivity and surface impedance result from the angular dependence of drift velocity should appear. For the directions of H_0, such that vD is close to zero, the intensity of cyclotron resonance is of the same order as the intensity of the resonance in a magnetic field parallel to the sample surface.
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