Analytical models are presented for the rates of layer thickness growth of MoSi2 and of Mo5Si3 that form by reaction of vapour-supplied Si with Mo or with partially silicided Mo. The models are applicable to other systems. Coupling of the diffusive flux of the reactive species Si with the rate of the chemical reactions determines the growth kinetics. The rate of chemical reaction is assumed to be proportional to the magnitude of a discontinuity in the Si activity at the physical boundary where the silicide reaction is occurring. Various combinations of diffusive versus chemical-kinetics-dominated transport in the two phases which grow in tandem are found to affect the functional dependence of the growth kinetics on time. Models include cases in which the host solid is heterogeneous, as occurs when the average composition of the host lies in a poly-phase region of the phase diagram.