Generalized predictive control (GPC) has been well-accepted in the chemical process industries because of its adaptive nature and ease of tuning. Nevertheless, the GPC structure is based on linear models, which can be a limitation for highly nonlinear processes often found in the chemical industry. A nonlinear generalized predictive control (NLGPC) algorithm was developed by Katende and Jutan (IEEE ACC Proceedings, Session FP10, Seattle, WA, 1995; Ind. Eng. Chem. Res. 1996, 35, 3539) and compared favorably to the standard GPC; however, the computational burden could be excessive in some cases. In this paper two quadratic forms of the NLGPC are developed on the basis of a second-order Hammerstein model structure and different criterion functions. These second-order models allow for simple on-line implementation and lay the basis for analytical evaluation of the algorithms. In this paper, simulation of sample problems are carried out and the effect of each criterion function used in the nonlinear controller design is discussed.