  Causality and stability in relativistic dissipative hydrodynamics are
important conceptual issues. We argue that causality is not restricted to
hyperbolic set of differential equations. E.g. heat conduction equation can be
causal considering the physical validity of the theory. Furthermore we propose
a new concept of relativistic internal energy that clearly separates the
dissipative and non-dissipative effects. We prove that with this choice we
remove all known instabilities of the linear response approximation of viscous
and heat conducting relativistic fluids. In this paper the Eckart choice of the
velocity field is applied.
