  In the one-dimensional isothermal case, we introduce a simple model of
nonlinear viscoelasticity within the Rational Extended Thermodynamics (RET)
framework. The differential system is determined by the universal principles of
RET, exhibiting symmetric hyperbolic form and ensuring the existence of smooth
solutions for appropriately small initial data. In the linear case, the
equation for viscous stress reduces to the well-known Maxwell model, thereby
representing a plausible nonlinear extension of the Maxwell-type model. The
total stress instead satisfies a non-linear Zener model.
