  We characterize the pairs of operator spaces which occur as pairs of Morita
equivalence bimodules between non-selfadjoint operator algebras in terms of the
mutual relation between the spaces. We obtain a characterization of the
operator spaces which are completely isometrically isomorphic to imprimitivity
bimodules between some strongly Morita equivalent (in the sense of Rieffel)
C*-algebras. As corollaries, we give representation results for such operator
spaces.
