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An adaptive nonlinear filter based on a second order Volterra series and on an IIR filter structure is presented. This filter is able to model higher than second order nonlinearities for systems where the nonlinearities are harmonically related. This solution represents an alternative to using higher than second order Volterra filters. We present a full derivation of this gradient search based adaptive nonlinear filter and also highlight the various assumptions and simplifications which require to be made in order to produce a practical algorithm. A comparison is made in terms of the performance and computational complexity between an adaptive second order IIR Volterra filter and an adaptive second and third order Volterra filters.