A new formulation of a block-structured model based on the Hammerstein operator is presented for the identification of multi-variate systems with input directionality. In contrast to the existing formulations for multi-variate Hammerstein models, the proposed structure offers the possibility to independently model the dynamic and nonlinear characteristics of the system and at the same time preserves the possibility to use the new efficient algorithms developed for the identification of single input Hammerstein models. Further, the formulation allows for a representation of arbitrary static nonlinear coupling of input variables with a considerably lower amount of parameters compared to existing formulations. The new model structure is applied to the identification of a fluid catalytic cracking (FCC) unit and significantly outperforms all previous multi-variate Hammerstein model structures by reducing the prediction error by over 50%. (C) 2006 Elsevier Ltd. All rights reserved.