[en] An experimental study of magnetic moments placed in a fourfold potential is presented here. The system used is a monocrystal of LiY_0.99Dy_0.01F₄, where the only magnetic ions are the Dy³⁺ ions. From static magnetic susceptibility measurements, it is shown that the Dy³⁺ ion has an easy magnetization plane, with an additional anisotropy in the easy plane. Low frequency electron paramagnetic resonance experiments are presented here and up to nine resonance lines have been found. Some of them are in agreement with known properties of the Dy³⁺ ion in LiY_0.99Dy_0.01F₄, but others cannot be explained within the framework of the commonly used effective Hamiltonian. The behaviour of these new lines is consistent with a magnetic tunnelling effect. Finally, spin echoes have been observed, allowing the determination of the relaxation time T₂ and the coupling coefficient for several orientations of the magnetic field