This article addresses the development of predictive transfer function models for nonlinear dynamic processes under serially correlated model error. This work is presented in the context of the block-oriented exact solution technique (BEST) for multiple input, multiple output (MIMO) processes proposed by Bhandari and Rollins (2003) for continuous-time modelling and Rollins and Bhandari (2004) for constrained discrete-time modelling. This work proposes a model building methodology that is able to separately determine the steady state, dynamic and noise model structures. It includes a pre-whitening procedure that is affective for the general class of discrete ARMA(p, q) noise (Box and Jenkins, 1976). The proposed method is demonstrated using a simulated physical system and a real physical system.