In the linear mechanics of viscoelastic bodies, wide use is made of the possibility of transforming from a description of elasticity to viscoelasticity by replacing elastic mechanical characteristics by appropriate time operators. The main factor ensuring this possibility is the property of linearity. Therefore, in considering nonlinear governing relations, the first question is whether it is possible in principle to transform from elasticity to viscoelasticity. We show that this transformation is possible and that it is based on general theorems of thermodynamics and the mathematical representations of nonlinear and linear functionals of tensor valued arguments.