A general mean field formalism for the two-component multilayer competitive growth processes by random irreversible deposition is presented. Overhangs and screening effects are ignored. The effects of the individual rates of the elementary act of deposition on the extent of growth, the overall growth rates (or currents) of the individual components and the composition at each deposited layer and in the bulk of the deposit are analysed. Transient and asymptotic behaviours of such quantities are derived. Various limiting growth situations of practical importance, namely poisoning of the growth of one component by the other, blocking of the multilayer growth by the monolayer coating of one of the components etc., are discussed in detail as special cases. Generalization of the formalism for more than two components is also indicated.