The minimal model structure detection (MMSD) problem in nonlinear dynamic system identification is formulated as a search for the optimal orthogonalization path. While an exhaustive search for a model with 20 candidate terms would involve 2.43 x 10(18) possible paths, it is shown that this can typically be reduced to 2 x 10(3) by augmenting the orthogonal estimation algorithm with genetic search procedures. The MMSD algorithm provides the first practical solution for optimal structure detection in NARMAX modelling, training neural networks and fuzzy systems modelling. Based on the MMSD algorithm, a refined forward regression orthogonal (RFRO) algorithm is developed. The RFRO algorithm initially detects a parsimonious model structure using the forward regression orthogonal algorithm and then refines the model structure by applying the MMSD algorithm to the reduced model term set. The RFRO algorithm cannot guarantee to find the minimal model structure, but it is computationally more efficient than the MMSD algorithm and can find a smaller model than the forward regression orthogonal algorithm.