  Recently we have proved the NRQCD factorization in heavy quarkonium
production at high energy colliders at all orders in coupling constant. In this
paper we extend this to non-equilibrium QCD and prove the NRQCD factorization
in heavy quarkonium production at all orders in coupling constant in
non-equilibrium QCD. This proof is necessary to study heavy quarkonium
production from quark gluon plasma at RHIC and LHC.
