A macroscopic model describing nonlinear viscoelastic waves is derived in Eulerian formulation, through the introduction of relaxation tensors. In the limiting case of small deformations, the governing equations recover those of the linear Zener model with memory variables, which is widely used in acoustics. The structure of the relaxation terms ensures that the model is dissipative. The chosen family of specific internal energies ensures also that the model is unconditionally hyperbolic. Numerical examples are proposed to illustrate the properties of viscoelastic waves, in small and large deformations.