  In this paper, we have established a general framework of multistage
hypothesis tests which applies to arbitrarily many mutually exclusive and
exhaustive composite hypotheses. Within the new framework, we have constructed
specific multistage tests which rigorously control the risk of committing
decision errors and are more efficient than previous tests in terms of average
sample number and the number of sampling operations. Without truncation, the
sample numbers of our testing plans are absolutely bounded.
