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This paper studies the standard problem for a class of multiple-delay systems, where different input/output channels have different dead times. We present a procedure of converting the original problem to an equivalent delay-free problem via loop-shifting arguments. This brings about and, for the first time, explains an unorthodox form of the dead-time compensator, called the feedforward action Smith predictor (FASP), in which an interchannel feedforward term is present alongside the conventional internal feedback. Our developments lead to a qualitative conclusion that the structure of the dead-time compensator should rely upon the structure of the regulated output and/or the way in which exogenous signals affect the measurement.