The magnetic and electronic structure of fee Fe/Cu bilayers were analyzed by means of the linear muffin-tin orbital (LMTO) method. We carried out ferromagnetic (FM) and non-magnetic (NM) calculations for several lattice spacings in order to obtain the total energy as a function of the volume. The FM state is energetically favoured over NM state by 5.5 mRy per atom. The analyses of the density of states gives a good description of the magnetic properties of these bilayers. The results show the collapse of the magnetism for certain critical lattice spacing, indicating the existence of more than one magnetic phase.