The present state of the evaluation of material balance data in the framework of international nuclear material safeguards is reviewed. The safeguards objectives, laid down qualitatively in the model agreement of the International Atomic Energy Agency, are formulated quantitatively in statistical terms as high probability of detection and short expected detection time in case of diversion. According to these objectives, the analysis consists of two parts: In the first part, a fixed reference time containing a given number of inventory periods is considered. Here, the optimal decision procedure can be determined explicitly. In the second part, an infinite reference time consisting of inventory periods of given lengths is considered. Here, only a general framework for the optimal decision procedure can be given so far; therefore, plausible procedures are discussed.