In this paper, we explore numerically the impact of different types of inter-layer coupling on the dynamics of a two-layer multiplex network of coupled FitzHugh–Nagumo oscillators in the excitable regime. For this purpose, the cases of attractive, repulsive, and periodically modulated inter-layer coupling are considered. Coupled in the ring structure, the FitzHugh–Nagumo neurons demonstrate travelling wave regimes which are different for the attractive and repulsive intra-layer coupling. It is shown that the inter-layer coupling affects not only the frequency of oscillations of individual neurons but also the spatio-temporal structures in individual layers in different ways, depending on the sign of the inter-layer coupling. It is established that complete in-phase synchronization of travelling waves is well achieved in the presence of attractive inter-layer coupling, while the repulsive inter-layer coupling induces effective anti-phase synchronization of wave regimes. When the inter-layer coupling is periodically modulated, the wave structures in both layers are distorted, and clusters of coherent and incoherent dynamics can appear in the ring space. The paper was presented at PhysCon2024.