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On the base of the analysis of results of experimental studies, an approach to the characterization of different nonlinear effects in the behavior of fibrous composite materials is proposed. One of them is concerned usually observed in experimental studies the dependence of deformation properties of composite materials on the type of external forces. Another type of nonlinearity lies in the fact that the shear stress-strain curves are nonlinear and the curvature of diagrams depends on the extent of shear strain, though they are linear ones when the load is applied along the reinforcement. The third type of nonlinearity is concerned the damage evolution and its influence on the stiffness characteristics that determines the fracture properties of composite materials. A good correspondence between theoretical dependencies obtained on the base of proposed models, numerical simulations and the results of experimental studies is shown.