We study the magnetization dynamics in a stray-field coupled pair of ferromagnetic squares in the vortex state. Micromagnetic simulations give an idea of the mediating stray field during vortex gyration. The frequency-dependent phase relation between the vortices in the spatially separated squares is studied using time-resolved scanning transmission x-ray microscopy while one element is harmonically excited via an alternating magnetic field. It is shown that the normal modes of coupled vortex-core motion can be understood as an attractive (low-frequency) and a repulsive (high-frequency) mode of the effective magnetic moments of the microstructures. Copyright 2012 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. {[}http://dx.doi.org/10.1063/1.4771683]