A generalization of the Rouse model of the dynamics of polymers in solution is proposed. The motion of long polymer chains is considered to be due to exponentially correlated random forces driving the polymer segments, which is a more realistic model than the approximation of white thermal noise in the standard theory. Due to the fluctuationdissipation theorem such a model is consistent with the assumption that the solvent has weakly viscoelastic properties, which corresponds to the theory, originally proposed by Maxwell and later substantiated coming from first principles. A consequence of such approach is the appearance of “memory” in the polymer dynamics. To obtain a correct description at short times, we also include inertial effects into the consideration. Discrete and continuum models of the universal dynamics of polymer chains are built. Exact solutions are obtained for the center of mass motion of the polymer coil in the discrete variant of the theory. The time correlation functions describing the dynamics of internal modes are calculated in the continuum approximation. The results significantly differ from those in the standard Rouse theory and its later generalizations valid at long times
