A titanium-silicon diffusion couple was used to measure the interdiffusion coefficients for TiSi2, TiSi, Ti5Si4, Ti5Si3 and Ti3Si at 950-1150 degrees C. The activation energy for the TiSi2 interdiffusion coefficient agrees with the data reported in the literature for thin film interdiffusion at lower temperatures. Diffusion-controlled, multi-layered growth kinetics set a constant ratio for the thickness of the TiSi2 layer to the total sum of thicknesses for the TiSi, Ti5Si4, Ti5Si3 and Ti5Si layers at a fixed temperature. The thickness ratio predicted from the Arrhenius temperature dependence for layer growth was compared with that experimentally observed at 700-1150 degrees C. Comparison of this thickness ratio with data reported for Ti-Si thin film growth indicates that only TiSi2 should form at low Temperatures. Competitive multi-layered kinetics decide that the low-temperature interdiffusion of Ti-Si thin films results in the exclusive growth of TiSi2, and consideration of nucleation or other constraints are not required to explain the absence of other Ti-silicide layers.