In this paper, an original result in terms of a sufficient condition to test the identifiability of nonlinear delayed-differential models with constant delays and multi-inputs is given. The identifiability is studied for the linearized system and a criterion for linear systems with constant delays is provided, from which the identifiability of the original nonlinear system can be proved. This result is obtained by combining a classical identifiability result for nonlinear ordinary differential systems due to Grewal and Glover (1976) with the identifiability of linear delayed-differential models developed by Orlov, Belkoura, Richard, and Dambrine (2002). This paper is a generalization of Denis-Vidal, Jauberthie, and Joly-Blanchard (2006), which deals with the specific case of nonlinear delayed-differential models with two delays and a single input. (C) 2010 Elsevier Ltd. All rights reserved.