This preliminary work aims at the formulation of the perturbative recursions for the HDMR component determination when the weight function is nonproduct type. The deviations from the product type, and, related items are used as the perturbing agents. By introducing a perturbation parameter to these terms serve us to expand the unknowns in powers of the perturbation parameter. Only the recursive equations are constructed here. The true implementations and algorithm construction has been left to future works.