  The structure of novel hydrodynamic model of plasmas with the relativistic
temperatures consisted of four equations for the material fields is presented
for the regime of anisotropic pressure and other tensors describing the thermal
effects. Presented model constructed of equation for evolution of the
concentration, the velocity field, the average reverse relativistic $\gamma$
functor, and the flux of the reverse relativistic $\gamma$ functor, which are
considered as main hydrodynamic variables. Four pressure-like tensors (two
second rank tensors and one fourth rank tensor) describe the thermal effects.
Among them we have the flux of the particle current and the current of the flux
of the reverse relativistic $\gamma$ functor. The high-frequency excitations
are considered analytically in order to trace the contribution of the
anisotropy of pressure-like tensors in their spectra.
