We report on a first, comprehensive partially quenched study of the eta-eta problem, based on SESAM configurations on a 16^3x32 lattice at beta=5.6 QCD with two (mass degenerate) active sea quark flavours. By means of the spectral approximation of the two-loop (hairpin) diagrams, we find clear plateau formation in the effective masses which enables us both to determine the eta-eta mass matrix and the alpha-parameter in the effective chiral Lagrangian for the flavour singlet sector, alpha=0.028 +- 0.013.