We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction, giving a prescribed two-electron density, has also been solved. The two-electron densities are found to lie in a convex set in a vector space. An algorithm to compute the ground-state energy of a few-particle system is proposed, based on the obtained results. (C) 2004 Elsevier B.V. All rights reserved.