This work is devoted to study of the strong selective reflection of obliquely incident laser beam (inclined geometry) from the interface "glass-rubidium vapour". It is shown that the contrast of the strongest refection resonances exceeds 500% at the moderate heating of reflecting cells. The new nonlinear properties of selective reflection resonances have been investigated - asymmetry of saturation of resonant total internal reflection (TIR) and nonlinear structures that appear under conditions close to resonant TIR. The observed structures can not be associated with well-known sub-Doppler resonances in selective reflection. The nonlinear structures described here do not have saturation properties in usual sense. They exist only in the inclined geometry and in a narrow range of saturating values of the surface power density at the interface. The transformation of the fluctuations of reflected light was also investigated at the optical saturation of selective reflection resonances. For this purpose the intensity of incident light was slightly modulated. The reduction of the corresponding intensity modulation was registered in the reflected light. This reduction of the intensity fluctuations ("classical squeezing") and the relatively high selective reflection coefficient offer good possibilities for the squeezing of quantum fluctuations in the reflected light. In the process of appropriate studies it was found that the reduction (squeezing) of photons (quantum) fluctuations in the reflected light beam is about of 5% in compare with the coherent light.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.