An important problem in system theory is whether a dynamic system is controllable with inputs from the class of admissible controls. This paper treats the case whore the dynamic system is described by differential-difference equations and the class of admissible control inputs consists of piecewise constant functions. This situation arises in practice in the on-line control of some industrial processes. Euclidean space and function space controllability are studied, and controllability conditions which are both necessary and sufficient are derived forRnandRnnull controllability. Simple algebraic conditions are also given for two special cases. In the study of function space null controllability the concept ofj-controllability is introduced and a sufficiency theorem is stated in terms of this new concept.