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The high-frequency response of two magnetostatically coupled nanodisks supporting a vortex state within a stack has been investigated by means of 3-D dynamic micromagnetic simulations performed in the frequency domain. These spectra reveal one or two resonance lines according to the vortex polarizations and chiralities. These sub-gigahertz resonance modes are associated with vortex core modes. The magnetostatic coupling controlled by the interdisk distance affects both the structure of the vortex core modes and their associated resonance frequencies. In the regime of strong magnetostatic interaction, coupled vortex core modes are analyzed in terms of the relative phase relation between the vortex core motions. Lastly, the characteristics of the dynamic susceptibility spectra are also strongly dependent on the relative disk thicknesses. It results that these dynamic magnetic couplings play a major role in the high-frequency response of layered magnetic nanostructures and should be taken into account in the design of new spintronic or microwave devices based on vortex dynamics.