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In this paper, we propose a new approach to identify a new class of nonlinear autoregressive models with exogenous inputs (NARX) based on kernel machine and space projection (KMSP). The well-known Hammerstein-Wiener model which includes blocks of nonlinear static functions in series with a linear dynamic block is a subset of the NARX models considered. In the KMSP based approach, kernel machine is used to represent the functions and space projection to separate the represented functions. We also discuss two possible ambiguities and give conditions to avoid such ambiguities. The asymptotic behavior of the proposed approach is analyzed. The performance of the proposed method is verified by simulation studies.