A solid-state reaction process in Ag/Al multilayer thin films has been investigated by the methods of in situ electron diffraction, simultaneous thermal analysis, transmission electron microscopy and X-ray diffraction with the aim of studying the phase formation kinetics of intermetallic compounds. The sequence of the phase transformations in the solid-state reaction has been established: Ag+Al→(Ag)+(Al)→(Ag)+δ-Ag₂Al→μ-Ag₃Al. The process of the solid-state interaction has been shown to consist of two steps; each of them is described by a kinetic model of the n^th order reactions with autocatalysis. The kinetic parameters of the autocatalytic process of the phase formation for δ-Ag₂Al and µ-Ag₃Al, have been determined, in particular, their apparent activation energy: 126 kJ/mol and 106 kJ/mol, respectively.