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An approach to the characterization of different types of nonlinearity in the behavior of composite materials is proposed. Some particular models are considered taking into account different types of nonlinearities. This approach is verified using complex loading experiments taken from a well-known World-Wide Failure Exercise and some other results of experimental studies. The theoretical dependencies obtained on the base of proposed models are compared with the results of experimental studies and good correspondence of them is shown. Such structure of proposed approach to the formulations of constitutive models from simple to more complex ones allows to demonstrate adequate description of the behaviour of composite materials under different loading conditions with the necessary precision.