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The filter-X LMS algorithm is successfully applied in linear active noise control and linear active vibration control. However, when it comes to nonlinear noise or vibration control, or the secondary path has a nonlinearity, this algorithm needs to be modified to ensure that it converges and that it is unbiased. We proposed configurations [V. DeBrunner, et al., 2003] that solve both the main path nonlinearity and the secondary path nonlinearity problems where the nonlinearity can be expressed by Volterra series. However, in practices some nonlinear system can be expressed in much simple form such as a linear filter followed by a memoryless nonlinearity (Wiener model), a memoryless nonlinearity followed by linear filter (Hammerstein model), a linear filter, a memoryless nonlinearity and another linear filter connected in series (LNL model). Such kinds of nonlinear system structure can greatly reduce the computation burden and simplify the implementation structure. In this paper, we give out active nonlinear noise control (ANNC) with these kinds of secondary path nonlinearity. We find with these kinds of nonlinear structure in the secondary path, the ANNC will have much simpler structure and the computation burden can be further reduced.