The coupling of electrochemical and optical measurements allows us to point out that the kinetics of coloration of amorphous tungsten trioxide thin films (a-WO3) is slower than the kinetics of the electrochemical reaction. However it is shown that the electrochemical reaction is controlled by a resistance R which depends on the conductivities of the electrolyte, the MxWO3 bronze, and the transparent electronic conducting sublayer. The molar absorption coefficients (at lambda=633 nm) of both LixWO3 and HxWO3 are determined. From the experimental results, a model is proposed to describe the mechanism of the electrochromic process in a-WO3. According to this model, the kinetics of coloration is found to be controlled by the diffusion into the oxide of an intermediate species (M+, e-). The oxidation of this species by a W6+ ion leads to the formation of an absorbing center and to the coloration of the oxide. The diffusion coefficients of (Li+, e-) and (H+, e-) as well as the rate constants k of the corresponding redox reactions are determined.