Abstract
The present paper is concerned with nonlinear systems that contain delays inside coupled with a part of state variables, which are often the cases in practical problems, but have not been treated yet. First we introduce an extension of the Lie derivative for a difference-differential equation; then we derive necessary and sufficient conditions for existence of a nonlinear feedback that linearizes the input-output behaviour of a system and decouples it from the delayed variables simultaneously. Discussions are given for two cases: firstly when the linearizing feedback contains only current values of state variables, and secondly when the linearizing feedback has memories to utilize the past values as well as the current values of state variables.
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