This paper gives a theoretical and experimental treatment of the subject. It is shown that the capture of single atoms can be related to catchment areas associated with stable and critical nuclei. It is then shown that for the materials and conditions used in evaporation work the size of the smallest stable cluster is normally a pair. Two equations describing the initial stages of growth are then derived dependent on whether the lifetime of single atoms is determined by reevaporation or by capture. For the reevaporation case, it is predicted that nucleation proceeds exponentially to a saturation density Ns of islands, and that Ns increases with temperature T and is independent of incidence rate R. For the capture case, condensation is initially complete and Ns increases with R and decreases with T. Experimental results with gold on vacuum cleaved rocksalt show reasonable agreement with the predicted behavior. Modified growth conditions are also examined experimentally, and the results are interpreted in terms of the parameters of the theoretical expressions. Growth using gold ejected from a sputtered single crystal suggests an increased effective condensate temperature. Normal evaporation with simultaneous electron bombardment of the substrate gives results which can be ascribed to lower mobility of migrating atoms.