The kinetics of ordering in fcc alloys during the growth of a (001) monolayer is investigated by the kineticmean-field method. The evolution of the structure parameters is calculated. There is a transient ordered stateduring the growth process and its occurrence depends on the ratio of the atomic exchange rate to the evaporationrate. The growth process displays two stages of evolution. The first stage is the formation of a metastableordered state whose lifetime increases exponentially with the decrease of the temperature. The second stage is the evolution from the metastable ordered state to the equilibrium ordered state. The stoichiometric concentrationsof the metastable ordered state is found to be different from the equilibrium one. The influence of thetwo characteristic times related to the adsorption and the atomic migration on the kinetics of the growth isanalyzed.