  We calculate the nucleonic and pionic dispersion relations at finite
temperature T and non-vanishing chemical potentials $(\mu_f)$ in the context of
an effective chiral theory that describes the strong and electromagnetic
interactions for nucleons and pions. The dispersion relations are calculated in
the broken chiral symmetry phase, where the nucleons are massive and pions are
taken as massless. The calculation is performed at lowest order in the energy
expansion, working in the framework of the real time formalism of thermal field
theory in the Feynman gauge. These one-loop dispersion relations are obtained
at leading order with respect to T and $\mu_f$. We also evaluate the effective
masses of the quasi-nucleon and quasi-pion excitations in thermal and chemical
conditions as the ones of a neutron star.
