The electronic structure of Ni/Au and Ni/Cu bilayers were calculated using the Linear Muffin-Tin Orbital (LMTO) method. The self-consistent calculations were made for several lattice parameters in order to obtain ground state properties of these bilayers. The analysis of the density of states at an equilibrium volume gives a good description of the electronic and magnetic properties. At Ni sites the magnetic moment is 0.49 mu(B) for Ni/Au bilayers and is zero for Ni/Cu bilayers. For the Ni/Au case a collapse of the magnetic moment at Ni sites is observed due to the shrinking of the lattice spacing.