A new algorithm, for identifying non-linear differential equation models, is introduced. The algorithm avoids the computation of derivatives by using the generalized frequency response functions to reconstruct the model. It is shown that the model can be constructed sequentially by building in first the linear terms, then the quadratic terms and so on and provides unbiased estimates in the presence of noise. A simulated example and the identification of a model relating the action of waveforces on an offshore structure are included to demonstrate the procedure.