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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.  We find two two‐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 there exist three two‐parameter families of the FitzHugh–Nagumo system for which the equilibrium point at  P  +  and at  P  −  is a zero‐Hopf equilibrium point. For one of these families, we prove the existence of one, two, or three periodic orbits starting at  P  +  and  P  − . Copyright © 2014 John Wiley & Sons, Ltd.

Zero‐Hopf bifurcation in the FitzHugh–Nagumo system