The dynamic behaviors of the process variables of a twin screw extruder (TSE) have inherent nonlinearity and time delay. Thus, it is important to develop a process model and furthermore to design controllers based on that model for stable operation. A new approach is explained in this work to develop dynamic gray box models to predict the responses of the process Output variables due to change in the screw speed (N) for a plasticating TSE. This approach comprises the selection of controlled variables and the development of gray box models relating the selected controlled variables and N. The selection of variables was based on both the steady-state correlation analysis with final product properties and the dynamic considerations. High-density polyethylenes with different melt indices were extruded in a co-rotating TSE in this work. A predesigned random binary sequence type excitation in N was imposed for the dynamic study. Gray box models were developed between two Output variables, melt temperature (T-melt) at die and melt pressure (P-melt) at die, with N, by incorporating both first principles knowledge of the process and the measured process data using the classical system identification technique. A second-order ARMAX (autoregressive moving average with exogenous input) model was found to be sufficient to capture the dynamic behaviors of T-melt when N was changed. However, the dynamic behavior of P-melt was modeled by a third-order ARMAX structure. Both models are in agreement with the a priori process information of the TSE.