  Limits of classical constitutive laws such as Fourier and Navier-Stokes
equations are discovered since decades. However, the proper extensions --
generalizations of these are not unique. They differ in the underlying physical
principles and in modeling capabilities. In this paper, two different theories
are discussed and compared to each other, namely the kinetic theory-based
Rational Extended Thermodynamics (RET) and non-equilibrium thermodynamics with
internal variables (NET-IV).
  First, the paper starts with the case of rigid heat conductors summarizing
the result achieved so far. Then a typical example of compressible bodies is
shown by presenting the first generalization for rarefied gases, called
Meixner's theory. It is further extended using generalized entropy current in
the framework of NET-IV. It is shown how its structure is related to RET and
how the compatibility between them can be acquired.
