Tests were performed on cyclic loading of the specimens made of ELUR-P carbon tape with the lay-up sequence [+45° / −45°]2s and cold-curing binder KhT-118. It has been established that when using viscoelasticity relations with Abel’s creep kernel, the ratio of viscous parts of strain at times shifted by values multiple to the load period does not depend on the amplitude and period of the cyclic load, the parameter that determines the degree of viscosity of the material, but depends only on the parameter determining the degree of attenuation of the creep process. The amount of energy absorbed in one loading cycle has the same property. It is shown that the independence of secant and tangent moduli from the absolute values of maximum and minimum stresses occurs for any kind of load and creep kernels using the linear theory of hereditary elasticity and a particular type of non-linear theory of viscoplastic flow with hardening. A method of sequential identification of creep kernel parameters, relations for viscoplastic and elastic strain based on the results of analysis of experimental data on cyclic loading is proposed. It is based on the hypothesis that at large creep times the rate of viscoplastic strain is much less than the rate of viscoelastic strain. This allows one, on the basis of theoretical results obtained for the Abel’s kernel, to obtain ratios from which it is possible, independently of other mechanical characteristics, to find the attenuation parameter from the strain values measured experimentally in times shifted by an integer number of periods. The method is illustrated by the example of data processing of real experiments conducted by the authors.