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 very much 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) under the condition that no neutrally stable equilibrium coordinates exist or they are only in the observed ones, the exact explicit solutions are in the same forms, furthermore the accelerative term will arise in the explicit solutions when parts of the coordinates participate in the entropy production; (2) under the condition that all the generalized thermodynamic coordinates participate in the entropy production, the term proportional to time will arise when only one neutrally stable equilibrium coordinate exists in the hidden ones and the generalized thermodynamic coordinates are given in the form of step function; (3) under the condition that the neutrally stable equilibrium coordinate exists in the hidden ones which participate in the entropy production, the accelerative term will arise in the explicit solutions when all of the observed coordinates and parts of the hidden ones participate in the entropy production regardless of the number of the neutrally stable equilibrium coordinates.