  We characterize the values of the parameters for which a zero--Hopf
equilibrium point takes place at the singular points, namely, $O$ (the origin),
$P_+$ and $P_-$ in the FitzHugh-Nagumo system. Thus we find two $2$--parameter
families of the FitzHugh-Nagumo system for which the equilibrium point at the
origin is a zero-Hopf equilibrium. For these two families we prove the
existence of a periodic orbit bifurcating from the zero--Hopf equilibrium point
$O$. We prove that exist three $2$--parameter families of the FitzHugh-Nagumo
system for which the equilibrium point at $P_+$ and $P_-$ is a zero-Hopf
equilibrium point. For one of these families we prove the existence of $1$, or
$2$, or $3$ periodic orbits borning at $P_+$ and $P_-$.
