The strong asymmetry in molecular dynamics between the two components of a binary mixture leads to a strong kinetic coupling between the stress field and the order parameter (concentration), which significantly affects the phase separation. A polymer solution, as a typical example of dynamically asymmetric mixtures, behaves as a gel in the initial stage of phase separation for a deep quench, while it behaves as a simple viscous fluid in the final stage. In the intermediate stage, the relaxational nature of the viscoelastic effect plays an important role in pattern evolution, which violates the self-similarity of the growing pattern. To understand the phenomena a concept of dynamic symmetry should be introduced in addition to the static composition symmetry.