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This paper discusses the optimum control of distributed parameter systems with time delays which are governed by a set of partial differential-difference equations. The technique of dynamic programming is used to derive the functional equations associated with optimization. Specific results are derived for linear systems with quadratic performance index. Also, an explicit condition for the complete null controllability of linear systems is given. The paper concludes with a discussion on the approximate solutions for the minimum energy control of a simple linear parabolic system with a time delay.