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The structure of novel hydrodynamic model of plasmas with the relativistictemperatures consisted of four equations for the material fields is presentedfor the regime of anisotropic pressure and other tensors describing the thermaleffects. Presented model constructed of equation for evolution of theconcentration, the velocity field, the average reverse relativistic $\gamma$functor, and the flux of the reverse relativistic $\gamma$ functor, which areconsidered as main hydrodynamic variables. Four pressure-like tensors (twosecond 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 fluxof the reverse relativistic $\gamma$ functor. The high-frequency excitationsare considered analytically in order to trace the contribution of theanisotropy of pressure-like tensors in their spectra.

Anisotropic pressure effects in hydrodynamic description of waves propagating parallel to the magnetic field in relativistically hot plasmas