Taking into account the aging effects the interconnected kinetic equations for the creep rate and damage parameter are formulated. The Maxwell equation, written in the scale of effective time, and the equation of the hereditary theory of visco-elasticity of Boltzmann-Volterra are used for the description of the degradation and destruction processes in polymer and composite materials. The analytical relations for creep, stress relaxation, damage parameter and the criteria of long-term strength are obtained. Corresponding theoretical curves are constructed and their qualitative agreement with the experimental curves is shown.