It has so far been believed that polymer systems belong to the same dynamic universality class as classical fluids, namely, the so-called model H in the Hohenberg-Halperin notation. However, our recent experimental studies strongly indicate that the behavior of polymer solutions can be explained by none of the conventional dynamic universality classes at least in the practical sense. Topological characteristics of polymer chains induces the slow molecular motion of polymer and the viscoelastic effect. The asymmetry in molecular dynamics between polymer and solvent leads to the strong kinetic coupling between the stress field and the order parameter. This causes the viscoelastic suppression of the order parameter fluctuation for equilibrium critical dynamics and unusual phase separation having a viscoelastically driven morphology for unstable states. The relaxational nature of viscoelastic effect violates the selfsimilarity of the growing pattern. A new concept of dynamic symmetry should be introduced in addition to the static, composition symmetry.