Magnetic vortices in permalloy squares are resonantly excited by alternating magnetic fields. By static external magnetic fields their equilibrium positions and trajectories are shifted. For gyrations far away from the center of the squares strongly elongated shapes of the resonant trajectories are observed by time-resolving x-ray microscopy. Within a simple analytical model which includes isotropic and anisotropic deviations from a parabolic potential elliptical trajectories are calculated. The directions of these ellipses coincide with the experimental observations. The experimental trajectories are also compared with micromagnetic simulations.