Results of Monte Carlo simulations carried out to examine the nature of the growth mechanism in MBE of lattice matched III–V compounds are presented. The role of surface molecular reaction kinetics associated with the dissociative chemisorption of the group V molecular specie is explicitly investigated for the first time and shown to lead to a new configuration‐dependent‐reactive‐incorporation (CDRI) growth process, quite distinct from the conventional notions of nucleation and continuous growth. For very slow dissociative reaction kinetics the CDRI growth process is shown to lead to a reaction‐limited‐incorporation (RLI) growth mechanism and the accompanying growth rate exhibits oscillatory behavior. For fast dissociative reaction kinetics, accompanied with a sufficiently fast surface interlayer migration kinetics of the group III atoms, the CDRI growth process gives rise to a configuration‐limited‐reactive‐incorporation (CLRI) growth mechanism. The crystal growth rate once again exhibits oscillations. It is also shown that under conditions involving specially delicate balance between the various kinetic rates, growth can proceed without oscillations in the growth rate. An essentially layer‐by‐layer mode of material addition is realized in all the aforementioned cases. Consequences of the resulting growth front morphology for the time dependence of the RHEED specular beam intensity are investigated and shown to give rise to a damped oscillatory behavior, including in the absence of oscillations in the crystal growth rate.