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This paper addresses the identification and control of nonlinear systems by means of Fuzzy Hammerstein (FH) models, which consist of a static fuzzy model connected in series with a linear dynamic model. For the identification of nonlinear dynamic systems with the proposed FH models, two methods are proposed. The first one is an alternating optimization algorithm that iteratively refines the estimate of the linear dynamics and the parameters of the static fuzzy model. The second method estimates the parameters of the nonlinear static model and of the linear dynamic model simultaneously by using a constrained recursive least-squares algorithm. The obtained FH model is incorporated in a model-based predictive control scheme and a new constraint-handling method is presented. A simulated water-heater process is used as an illustrative example. A comparison with an affine neural network and a linear model is given. Simulation results show that the proposed FH modeling approach is useful for modular parsimonious modeling and model-based control of nonlinear systems.