We propose a dual-adatom diffusion-limited model for the growth of compound semiconductor nanowires via the vapor-liquid-solid or the vapour-solid-solid mechanisms. The growth is catalyzed either by a liquid or a solid nanoparticle. We validate the model using experimental data from the growth of InAs nanowires catalyzed by a gold nanoparticle in a molecular beam epitaxy reactor. Initially, we determine the parameters (diffusion lengths, flux to the seed, Kelvin effect) that describe the growth of nanowires under an excess of one of the two beams (for instance, group III or group V atoms). The diffusion-limited model calculates the growth rate resulting from the current of atoms reaching the seed. Our dual-adatom diffusion-limited model calculates for a compound semiconductor, the instantaneous growth rate resulting from the smallest current of the two types of atoms at a given time. We apply the model to analyze the length-radius dependence of our InAs nanowires for growth conditions covering the transition from the As-limited to the In-limited regime. Finally, the model also describes the complex dependence of the transition between both regimes on the nanowire radius and length. This approach is generic and can be applied to study the growth of any compound semiconductor nanowires.