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The article deals with the problem of a layered composite pipe. The layers alternate in pairs and consist of elastic-creeping materials. The work is devoted to the study of the mechanical properties of the composite material with the help of its microstructure. Processes are studied with a typical pipe radius which is much more than the typical winding width. Heterogeneous layered material behaves as a certain "effective" material without layers in such processes. The method of calculation of effective moduli based on mathematical homogenization theory is described. Creep kernels are given by the sum of a finite number of decreasing exponential functions.