A generalized viscoelastic constitutive theory in which visco-elasticity and plasto-elasticity were unified was established based on the elemental discipline of thermodynamics and the principle of maximum Homiltons dissipation rate.  Convex analysis demonstrated  that the principle of maximum Homiltons dissipation rate in the internal strain rate space is equivalent to the principle of maximum Lagranges dissipation rate in the internal stress space. When the function of Homiltons dissipation rate is an Eulers homogenous function of degree one in internal strain rate, viscoelasticity is degenerated into plasto-elasticity and the principle of maximum Lagranges dissipation rate is degenerated into the principle of Hills maximum plastic work. Therefore, plastic behavior is a specific case of generalized viscosity. Quasi-Maxells models and quasi-Kelvins models and quasi-critical state visco-elastic models are derived respectively from different free energy functions and different dissipation rate functions by the principle of maximum Homiltons dissipation rate and the principle of maximum Lagranges dissipation rate. It is proved that as their dissipation rate function are Eulers homogeneous functions of degree one, the generalized Von Mises yield criterion and the generalized Von Mises linear kinematic hardening criterion and Wei Ru-longs critical state yielding criterion are specific cases of quasi-Maxwells models and quasi-Kelvins models and quasi-critical state visco-elastic models respectively. The value results and charts  visually verified the reliability of above-mentioned conclusions.