  We introduce a parametrization of the coupling constant space of the
generalized Kontsevich models in terms of a set of moments equivalent to those
introduced recently in the context of topological gravity. For the simplest
generalization of the Kontsevich model we express the moments as elementary
functions of the susceptibilities and the eigenvalues of the external field. We
furthermore use the moment technique to derive a closed expression for the
genus zero multi-loop correlators for $(3,3m-1)$ and $(3,3m-2)$ rational matter
fields coupled to gravity. We comment on the relation between the two-matrix
model and the generalized Kontsevich models
