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−