  In this work we consider the role of muons in various URCA processes relevant
for neutrino emissions in the core region of neutron stars. The calculations
are done for $\beta$--stable nuclear matter with and without muons. We find
muons to appear at densities $\rho = 0.15$ fm$^{-3}$, slightly around the
saturation density for nuclear matter $\rho_0 =0.16$ fm$^{-3}$. The direct URCA
processes for nucleons are forbidden for densities below $\rho = 0.5$
fm$^{-3}$, however the modified URCA processes with muons $(n+N\rightarrow p+N
+\mu +\overline{\nu}_{\mu}, p+N+\mu \rightarrow n+N+\nu_{\mu}$), where $N$ is a
nucleon, result in neutrino emissivities comparable to those from
$(n+N\rightarrow p+N +e +\overline{\nu}_e, p+N+e \rightarrow n+N+\nu_e$). This
opens up for further possibilities to explain the rapid cooling of neutrons
stars. Superconducting protons reduce however these emissivities at densities
below $0.4$ fm$^{-3}$.
