The decoupling problem is solved for anm-inputm-output linear time-invariant system with multiple delays in the state and/or the control. The conditions under which such a system can be decoupled are found and the class of the feedback decoupling operators is given. These operators are realized by means of digital filters. Then, the more general linear model in which the input effects directly the output is considered which, upon the introduction of both feedback and feedforward, is shown to be decoupled, Two illustrative examples are included to support the theoretical results.