We consider the situation where a nonlinear physical system is identified from input-output data. In case no specific physical structural knowledge about the system is available, parameterized grey box models cannot be used. Identification in black-box-type of model structures is then the only alternative, and general approaches like neural nets, neuro-fuzzy models, etc., have to be applied.However, certain non-structural knowledge about the system is sometimes available. It could be known, e.g., that the step response is monotonic, or that the steady-state gain curve is monotonic. The question is then how to utilize and maintain such knowledge in a black box framework.In this paper we show how to incorporate this type of prios information in an otherwise black box environment, by applying a specific fuzzy model structure, with strict parametric constraints. The usefulness of the apporach is illustrated by experiments on real-world data.