For astrophysical phenomena, especially in the presence of strong gravity, the causality of any phenomena must be preserved. On the other hand, dissipations, e.g. heat flux and bulk and shear viscosities, are necessary in understanding transport phenomena even in astrophysical systems. If one relies on the Navier-Stokes and Fourier laws which we call classic laws of dissipations, then an infinite speed of propagation of dissipations is concluded (14). (See appendix 7 for a short summary.) This is a serious problem which we should overcome, because the infinitely fast propagation of dissipations contradicts a physical requirement that the propagation speed of dissipations should be less than or equal to the speed of light. This means the breakdown of causality, which is the reason why the dissipative phenomena have not been studies well in relativistic situations. Also, the infinitely fast propagation denotes that, even in non-relativistic case, the classic laws of dissipations can not describe dynamical behaviors of fluid whose dynamical time scale is comparable with the time scale within which non-stationary dissipations relax to stationary ones. Moreover note that, since Navier-Stokes and Fourier laws are independent phenomenological laws, interaction among dissipations, e.g. the heating of fluid due to viscous flow and the occurrence of viscous flow due to heat flux, are not explicitly described in those classic laws. (See appendix 7 for a short summary.) Thus, in order to find a physically reasonable theory of dissipative fluids, it is expected that not only the finite speed of propagation of dissipations but also the interaction among dissipations are included in the desired theory of dissipative fluids. Problems of the infinite speed of propagation and the absence of interaction among dissipations can be resolved if we rely not on the classic laws of dissipations but on the Extended Irreversible Thermodynamics (EIT) (13; 14). The EIT, both in non-relativistic and relativistic situations, is a causally consistent phenomenology of dissipative fluids including interaction among dissipations (9). Note that the non-relativistic EIT has some experimental grounds for laboratory systems (14). Thus, although an observational or experimental verification of relativistic EIT has not been obtained so far, the EIT is one of the promising hydrodynamic theories for dissipative fluids even in relativistic situations. 1