Ultrathin Au1-cNic alloys have been grown at room temperature by molecular beam epitaxy on Au(001) buffer layers. The Ni concentration c, ranging from 0.2 to 0.4, is much higher than the bulk solubility. The structural evolution with temperature has been investigated by X-ray diffraction measurements. The AuNi layer is coherently strained on the Au buffer and a modulated structure develops along the growth direction upon annealing at 220 degrees C. The period of the modulation is around 6-8 Angstrom and gives rise to satellite peaks. A simulation has shown that these peaks may be reproduced by a superlattice cell in which monoatomic Ni planes are separated by three or four Au atomic planes. At higher temperatures, there is a diffusion of Ni in the surrounding Au regions, leading to a homogeneous and dilute AuNi solid solution.