This paper introduces an original definition of diagnosability for nonlinear dynamical models called functional diagnosabillty. Fault diagnosability characterizes the faults that can be discriminated using the available sensors in a system. The functional diagnosability definition proposed in this paper is based on analytical redundancy relations obtained from differential algebra tools. Contrary to classical definitions, the study of functional diagnosability highlights some of the analytical redundancy relations properties related to the fault acting on the system. Additionally, it gives a criterion for detecting the faults. Interestingly, the proposed diagnosability definition is closely linked to the notion of identifiability, which establishes an unambiguous mapping between the parameters and the output trajectories of a model. This link allows us to provide a sufficient condition for testing functional diagnosability of a system. Numerical simulations attest the relevance of the suggested approach. (C) 2015 Elsevier Ltd. All rights reserved.