In this article, a novel identification framework is proposed to capture a class of nonlinear dynamic relationships that link several input signals (and their past values) to a single output. The class of relationships is the one in which the single output to be identified may be any monotonic nonlinear function of a linear regressor that may be built up with the input signals and their past values. This obviously recalls the known Wiener identification structure with differences that are underlined in the article. The whole framework is validated using the difficult problem of deriving real data-based dynamic model of emissions (including NOx and particulate matter) of a diesel engine. The compelling feature of the proposed approach lies in the fact that the underlying optimization problem to be solved is a constrained quadratic programming problem and this, despite the nonlinear character of the identified relationship.