  In this paper, we revise Maxwell's constitutive relation and formulate a
system of first-order partial differential equations with two parameters for
compressible viscoelastic fluid flows. The system is shown to possess a nice
conservation-dissipation (relaxation) structure and therefore is symmetrizable
hyperbolic. Moreover, for smooth flows we rigorously verify that the revised
Maxwell's constitutive relations are compatible with Newton's law of viscosity.
