Radiation-induced precipitation of a new phase at the surface of an alloy during irradiation at elevated temperatures was studied with the aid of a kinetic model of segregation. The preferential coupling of solute atoms with the defect fluxes gives rise to a strong solute enrichment at the surface, which, if surpassing the solute solubility limit, leads to the formation of a precipitate layer. The moving precipitate/matrix interface was accommodated by means of a mathematical scheme that transforms spatial coordinates into a reference frame in which the boundaries are immobile. Sample calculations were performed for precipitation of the γ'-Ni 3Si layer on Ni-Si alloys undergoing electron irradiation. The dependences of the precipitation kinetics on the defect-production rate, irradiation temperature, internal defect sink concentration and alloy composition were investigated systematically.