In this paper, an original result in terms of a sufficient condition to test 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 M.S. Grewal and K. Glover [4] with the identifiability of linear delayed-differential models developed by Y. Orlov et al. [10]. This paper is a generalization of [2], which deals with the specific case of nonlinear delayed-differential models with two delays and a single input. Key words: Key words - Identifiability, Nonlinear delayed-differential models.