Many models in Systems Biology are described as a system of Ordinary Differential Equations. The fact that the Systems Biology Markup Language SBML has become a standard for sharing and publishing models, has helped in making modelers formalize the structure of the reactions and use structure-related methods for reasoning about models. Unfortunately, SBML does not enforce any coherence between the structure and the kinetics of a reaction. Therefore the structural interpretation of models transcribed in SBML may vary according to different choices of representation of the original model and may be incorrect for some analyses. The first contribution of this paper is to propose a general compatibility condition between the kinetic expression and the structure of a reaction. We show that these well-formedness conditions are satisfied by standard kinetics and that they entail a property of independence from the kinetic expressions for the influence graph associated to the ODEs. We present a heuristic algorithm of low computational complexity for, given an ODE system, inferring a reaction model that preserves the ODE semantics and infers well-formed reactions whenever possible. This algorithm can be used for not only checking whether the network and ODE structures of an SBML model are consistent but also automatically curating SBML models by exporting them as ODE systems and then importing them as well-formed reaction models. We show how this strategy is capable of automatically curating SBML models on a large scale and provide some statistics figures obtained on the whole biomodels.net repository. The algorithms described in this paper are implemented in the open-source software modeling platform BIOCHAM [Fages and Soliman, 2008a, Calzone et al., 2006] available at http://contraintes.inria.fr/biocham The models used in the experiments are available from http://www.biomodels.net/