The modifications of the effective elastic constants of sputter-deposited Ag/Ni superlattices under annealing are studied by use of the Brillouin light-scattering technique. At-temperature measurements, taken while annealing the specimens, made it possible to study the dynamical evolution of the structure under investigation, through detection of up to four guided acoustic modes. Measurements taken at room temperature, after isochronal and isothermal cycles, permitted achievement of a deeper understanding of the variations of the elastic properties. It has been found that those elastic constants that are sensitive to interface effects, namely cM and c33, are also markedly modified during the thermal treatment; no appreciable variation of cl1 has been measured. The observed variations of the elastic constants are interpreted on the basis of the structural informations gained by use of x-ray and transmission electron microscopy; a comparison is also made with electrical resistivity results. 3028