Overall dynamic response and creep behavior of random multi-component composites with nonlinear constituents are investigated. As in Rabotnov's  type theory, the behavior of the viscoelastic material is described by a quasi-linear law. The nonlinear function of instant elastic stress plays the role like that of the strain in the linear case. We use constitutive equations for statistical fluctuations of first and second order displacement, nonlinear Green deformation, nominal or Cauchy stress in the representative volume. Upon application of the integral Carson and Fourier transforms, the boundary value problem for the local stress and strain fields becomes similar to a linear elastic problem. The programs from NAG-Fortran library are used. The model suggested may be useful for long-term durability prediction under cyclic loading.