This study deals with data-driven modelling of deterministic discrete-time non-affine nonlinear systems based on a novel neurofuzzy framework. The neurofuzzy architecture is inspired by the Adaptive Neurofuzzy Inference System topology and it consists of seven layers. The premise subspace is represented by the concatenation of states and exogenous inputs while the consequent subspace is described by local linear state-space models. The proposed neurofuzzy model is shown to be a universal approximator on compact sets. Experiments on a non-affine nonlinear system demonstrates the feasibility and effectiveness of the proposed neurofuzzy model structure for system identification.