In recent years, the interest has grown in nonlinear integral equations of convolution type in connection with their application in various fields of mathematical physics, inparticular, inthep-adic theory of an open-closed string, kinetic theory of gases, in the theory of radiation transfer in spectral lines. The paper is devoted to the questions of construction of nontrivial solutions and the study of their asymptotic behavior for one system of nonlinear integral equations of convolution type with a symmetric kernel on the whole axis.
