  Following the basic prescriptions of the Tsallis' nonextensive
thermodynamics, we study the relativistic nonextensive thermodynamics and the
equation of state for a perfect gas at the equilibrium. The obtained results
are used to study the relativistic nuclear equation of state in the hadronic
and in the quark-gluon plasma phase. We show that small deviations from the
standard extensive statistics imply remarkable effects into the shape of the
equation of state.
