We have investigated the composition and growth kinetics of hafnium silicides (HfSi and HfSi2) formed from thin films of hafnium sputter deposited on silicon. Backscattering of MeV He ions was used to monitor the growth of the silicide phases and to determine the Si/Hf concentration ratios. Seemann-Bohlin x-ray diffraction techniques provided identification of the phases and an estimate of the crystallite size of the films. The stable-phase HfSi forms in the temperature region 550-650°C. The reaction initiates at the Hf/Si interface and the thickness of the HfSi increases proportional to the square root of time. The HfSi grows by diffusion of Si through the already formed phase with an interdiffusion constant D ≃ 2.4 exp(-EA/k T) cm2/sec with EA = 2.5 eV. Different behavior is observed for the formation of the HfSi2. In this case the silicide forms simultaneously throughout the HfSi layer at temperatures above 750°C. We propose that the HfSi2 nucleates at the grain boundaries of the HfSi, rather than at the Si/HfSi interface. The transition to HfSi2 is completed rapidly because of the large density of nucleation sites and the small grain size of the film.