In recent years, various sequential procedures have been proposed for application in Near Real Time Accountancy (NRTA) in the framework of international nuclear material safeguards. Since there is no single objective for safeguards - the requirement for a most sensitive as well as timely detection cannot be achieved simultaneously - these procedures have to be compared numerically for selected loss/diversion patterns on the basis of reasonable data. In this paper, the most common procedures are classified, their main properties are discussed and their average detection times (average run lengths in terms of inventory periods) are calculated numerically for the protracted loss/diversion pattern with the help of the idealized data of an industrial-scale reprocessing plant. Practical conclusions are not drawn, instead, the way one might arrive at a final selection of a ''best'' test procedure is discussed.