The thermal stability of sputter-deposited Mo/Si multilayers was investigated by annealing studies at relatively low temperatures for various times. Two distinct stages of thermally-activated MoSi interlayer growth were found: a relatively rapid initial "surge" of approximately one monolayer, followed by a (slower) secondary "steady-state" growth that is diffusion controlled. The interdiffusion coefficients for the interlayer formed during deposition of Mo on Si are substantially higher than those of the interlayer formed during deposition of Si on Mo. It was also observed that significant residual tensile elastic strains develop within the Mo layer (normal to the multilayer) as a result of annealing. Explanations for these observed behaviors are presented.