SUMMARY One of the major difficulties associated with the chemical separation usually required in activation analysis for trace elements has been the need to determine the chemical yield of the separation process. In a separation using the substoichiometric principle, equal amounts of a reagent capable of converting the irradiated element and its isotopic carrier to an easily-separable form are added to the prepared sample and to the standard, but the reagent is sufficient to react with only a part of the element and carrier which is present. By this means the specific activities of the extracts or precipitates are made proportional to the total activities, and the determination of the absolute chemical yield of the separation is rendered unnecessary. Furthermore, the use of a substoichiometric amount of reagent usually increases the selectivity of the separation process. The principle can be applied with equal, or even greater, advantage to radioisotope dilution analysis, and its use has greatly extended the application of tracer methods to the analysis of elements at microgram and submicrogram levels. Of the methods which have been adapted for substoichiometric separations of elements, the most common are the solvent extraction of metal chelates and of ion-association compounds, and the ion-exchange separation of soluble complexonates. Precipitation methods have also been used, and both electrolysis and replacement substoichiometry are likely to increase in importance. Substoichiometric methods have been applied with success to the analysis of many metals at trace level in a variety of materials; methods for the analysis of non-metals are also beginning to be developed. Perhaps substoichiometry will make its greatest impact in the development of isotope dilution analysis, a technique which has been neglected for trace analysis in the past because of the need to determine chemical yields. This development is particularly to be welcomed because it extends radioanalytical methods to laboratories which do not have easy access to nuclear reactors for neutron-irradiation.