  We consider a general causal relativistic theory of divergence type in the
framework of Rational Extended Thermodynamics (RET) for a compressible,
possibly dense, gas. We require that the system converges in the Maxwellian
iteration's first step to the parabolic Eckart equations. This requirement
implies a constraint between the two coefficients present in the triple tensor
evaluated at equilibrium. Moreover, the production tensor is determined for
prescript thermal and caloric state equations and given heat conductivity,
shear, and bulk viscosities. In the second part, we prove that if the original
hyperbolic system satisfies the universal principles of RET, as can be put in
the symmetric form using the \emph{main field}, it always satisfies the
previous compatibility condition. Therefore any causal system of divergence
type that satisfies the entropy principle with a convex entropy converges to
the Eckart system in the Maxwellian iteration also when we have no information
at the mesoscopic scale from the kinetic theory.
  The obtained results are tested on the RET theories of rarefied monatomic and
polyatomic gases.
