Although the average composition change resulting from O or N implantation in a metal is small up to a dose of about 3 × 1016ions/cm2, the implanted atoms tend to be atomically mobile under the conditions used for bombardments and precipitation of an oxide or nitride can be expected. The object of this work is to explain what phases are formed. One model is based on the postulate that the precipitates are at the surface and have a high anion-to-cation ratio. The resultant phase therefore tends to be that which arises from the impact of any heavy particle on the surface of a high oxide or nitride. An alternative model is based on the postulate that the precipitates tend, independently of where they form, to be in qualified thermodynamic equilibrium with the metal. A consideration of the known examples of O or N implantation suggests that qualified thermodynamic equilibrium is the better guide to which phases are formed.