Abstract: A new theoretical system of viscoelasticity, which includes the traditional linear viscoelasticity as its special case, is proposed in this paper. The main results of this theory are two elasticity recovery correspondence principles, which are used for solving a class of physically nonlinear viscoelastic problems. By means of which, the solution of a nonlinear viscoelastic problem can be obtained if the solution of the corresponding nonlinear elastic problem is known. Correspondence principles are not based upon the similarity of the constitutive relations. Rather, they are based upon the recoverability from the present viscoelastic responses to the instantaneous elastic responses. The correspondence between the nonlinear viscoelastic and the nonlinear elastic constitutive relations is found first, and then two elasticity recovery correspondence principles are deduced. It is shown by the experiments for improved polypropylene that these principles are valid and are applicable to such class of materials.