<p>A four-dimensional family of vector fields, consisting of two identical FitzHugh-Nagumo systems linearly coupled by diffusion, is considered. The focus is placed on codimension-two Hopf-Hopf bifurcations unfolded by the coupled system. We identify seven of the eleven possible cases of Hopf-Hopf bifurcations. The bifurcation diagram for two of these cases reveals the emergence of quasi-periodic dynamics, characterized by the presence of two-dimensional and three-dimensional invariant tori. We examine these specific cases in greater detail by studying the associated local bifurcations through concrete examples and presenting relevant numerical simulations. The dynamical richness, extending beyond the local bifurcation diagrams, is further emphasized through additional numerical explorations.</p>