The production of J/ψ-pairs as a possible measure of the polarized gluon
distribution ΔG(x) is studied for proton--nucleon collisions at
\sqrt{s} =40\;\mbox{GeV}^2 (HERA-N). Possibilities of
reconstructing the helicity state of at least one of the J/ψ's are
critically reviewed. The observation of production asymmetries in the single
polarized mode of HERA-N is found to be not feasible.Comment: 8 pages, LATeX, 3 figures availabe as .uu-fil