Block-oriented modeling approaches to the development of NARMAX models for processes exhibiting output multiplicities are introduced "Feedback block-oriented" model structures are proposed that can force the resulting NARMAX model to have a particular steady-state behavior and reduce the model-identification problem to a constrained, linear model identification. These models are particularly suitable for gray-box modeling approaches where it is assumed that the steady-state behavior of the process is known and a NARMAX model is sought to approximate its dynamic response. The proposed approaches are applied to a CSTR model with three steady states to illustrate their performance.