  Approximate solution of the ensemble representability problem for density
operators of arbitrary order is obtained. This solution is closely related to
the ``Q condition'' of A.J.Coleman. The representability conditions are
formulated in orbital representation and are easy to use. They are tested
numerically on the base of CI calculation of simple atomic and molecular
systems. General scheme of construction of the contraction operator right
inverses is proposed and the explicit expression for the right inverse
associated with the expansion operator is derived as an example. Two algorithms
for direct 2-density matrix determination are described.
