The noninferior vector index problem of optimal control theory is investigated in an effort to establish some basic properties of the noninferior index surface in the generalN-dimensional index problem. The vector performance index problem is first converted to a family of scalar index problems by forming an auxiliary scalar index as a function of the vector index and a vector of weighting parameters. The functional relationship between noninferior vectors and the weighting vectors of the auxiliary index problem is investigated for the particular case in which the auxiliary index is a weighted sum of the vector index elements. Special attention is devoted to the noninferior index problem for whichN = 2.