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Differential linear repetitive processes are a distinct class of 2D continuous-discrete linear systems of both applications and systems theoretic interest. In applications, they arise in iterative learning control schemes and in iterative solution algorithms for nonlinear dynamic optimal control algorithms based on the maximum principle. Repetitive processes cannot be analysed/controlled by direct application of the existing systems theory and hence a 'mature' systems theory must be developed for them followed (where appropriate) by onward translation into efficient controller design algorithms. This paper continues the development of the former area by developing some significant new results on the application of currently available delay differential systems theory to these processes.