Sufficient conditions for the perfect aggregation of linear programming models were given by Day in 1963. Essentially the same set of conditions was shown to be necessary by Guccione and Oguchi in 1977.1 Here we extend these results to quadratic programming systems, a natural first step in the study of consolidation for more general nonlinear programming models. We assume that the reader is familiar with Ijiri's excellent survey of the aggregation problem, aware of its general structure, and thus of its relevance to economists.