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This paper presents an output-sliding mode control (OSMC) design method for a class of nonlinear multi-delay systems. Combining the differential geometry approach with the approximating variable structure control method, the output-sliding mode controller is presented, which yields reduced-order subsystems exhibiting equivalent dynamics. The switched control law forces the systems' trajectory and maintains it on the sliding surface, where the output variables are decoupled from the inputs and the time-delays. These sliding subspaces are considered linear systems under the proper coordinate transformation, where the further control aims could be realized under the pole placement method. The sliding mode equations of the system are presented as well.