A kinetic model of semiconductor nanowire growth by gas phase adsorption is developed taking into account, along with the surface equilibrium diffusion of adatoms, the nonequilibrium diffusion of excited (hot) atoms generated by acts of adsorption and their relaxation as a result of excitation-energy accommodation via an electron channel at catalyst droplets. The processes that occur on the surface are simulated using the stochastic Monte Carlo method. It is shown that hot-adatom relaxation can determine the nanowire growth rate. The conditions for nanowire growth by the equilibrium or nonequilibrium diffusion of adatoms are established. It is demonstrated that the nanowire growth rate depends on the diameter of the nanodroplets, the distance between them, and the mean free path of atoms excited by the act of adsorption.