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Problem of constructing an effective model of a layered composite material is considered. The layers consist of elastic-creeping materials, the creep kernels of which are exponents. The characteristics of the averaged model are given in explicit form. Some qualitative properties of the homogenized model are analyzed. Estimates of the closeness of the displacement and stress fields for the initial and averaged models are given. An example of numerical modeling of the characteristics of an averaged material is presented. The exact number of constants required for a complete description of the averaged model is given.