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In this paper a quite general formulation of sequential pattern recognition processes is presented. Within the framework of this formulation, a procedure is obtained for the simultaneous optimization of the stopping rule and the stage-by-stage ordering of features as the process proceeds. This optimization procedure is based on dynamic programming and uses as an index of performance the expected cost of the process, including both the cost of feature measurement and the cost of classification errors. A simple example illustrates the important computational aspects of the procedure and indicates the form of the solution.