Abstract: It is obvious that the exact solutions of the evolution equation, which is derived by regarding the deformation process of viscoelastic materials as an irreversible thermodynamic process, depend verymuch on the properties of their coefficient matrices. These matrices are usually affected by the nature of the generalized thermodynamic coordinates, which leads the solutions for the generalized thermodynamic coordinates to that: (1) the term proportional to time will arise when only one neutrally stable equilibrium coordinate exists in the coordinates participating in the entropy production; and (2) the generalized thermodynamic forceswill be replaced by the equivalent generalized thermodynamic forceswhen parts of the observed generalized thermodynamic coordinates participate in the entropy production.