  Extended theories are widely used in the literature to describe the
relativistic fluid. The motivation for this is mostly due to the causality
issues allegedly present in the first order theories. However, the decay of
fluctuations in the system is also at stake when first order theories
\emph{that couple heat with acceleration} are used. In this paper it is shown
how the generic instabilities in relativistic fluids are not present when a
Maxwell-Cattaneo type law is introduced in the system of hydrodynamic
equations. Emphasis is made on the fact that the stabilization is only due to
the difference in characteristic times for heat flux relaxation and
instabilities onset. This gives further evidence that Eckart's like
constitutive equations are responsible for the first order sytem exhibiting
unphysical behavior.
