We report on the structural stability upon annealing of (0 0 1) Au/Ni artificially modulated structures (AMS) grown by molecular beam epitaxy (MBE). The structural evolution of samples with a nominal periodicity of 2, 6 and 7 monolayers (ML) and Ni atomic fractions of 0.4 and 0.5 has been investigated by in situ X-ray Diffraction and compared with what occurs for AuNi solid solutions of the same compositions, for which a modulated structure with a periodicity between 3 and 4 ML along the growth direction has been reported previously. The effect of the epitaxial strain imposed by the buffer layer on which the AMS is deposited has also been studied. It is shown that, whatever the nominal period is, the AMS evolve towards a modulated structure having a similar to3 ML period, provided that the epitaxial strain is high enough. These experimental results are explained in terms of an epitaxial-strain-stabilized ordering, as supported by numerical simulations.