This paper describes a gray-box identification approach to three classes of block-oriented models: Hammerstein models, Wiener models, and the feedback block-oriented models introduced recently for modeling processes with output multiplicities. Here, we restrict consideration to processes with nonlinear steady-state characteristics that are known a priori and do not exhibit steady-state multiplicities. Under this assumption, simple identification procedures may be developed for all three of these model structures, which may be viewed as three different ways of combining a single static nonlinearity with a linear dynamic model with specified steady-state gain constraints. In particular, if the steady-stare gain of the linear dynamic model is constrained to be I, the steady-state characteristic of the overall model is determined entirely by the static nonlinearity. If the steady-state characteristic of the process is known, the nonlinear component of the model may be determined from this knowledge, and the parameters of the linear model may be estimated from input-output data. Detailed descriptions of simple least squares solutions of this identification problem are presented, and the approach is illustrated for a simple first-principles model of a distillation column. (C) 2000 Elsevier Science Ltd. All rights reserved.