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This paper demonstrates methods for applying combined optimum control and estimation theory to serial systems with time delay. The case of serial linear systems with time delay is considered in detail; a result analogous to the separation theorem of linear systems is presented. Illustrative examples of serial chemical reactors, rolling mills, and second-order plus dead-time approximations of higher order systems are discussed. Numerical results for a second-order plus dead-time system are presented: these results are compared with a suboptimal feedback controller (modified Smith predictor) and the open-loop response. It is shown that, in this case, the optimum estimation and control gains may be approximated by constants which further simplify the DDC algorithm. In the second-order plus dead-time approximation to higher order overdamped systems, the optimum algorithm can be reduced to recursive estimation with constant gain and linear state variable feed forward control. This algorithm may be used as a direct replacement for digital controllers used in the process industries.