  A calculation of the loop-induced gluon-fusion process gg -->
Z(photon)Z(photon) --> l anti-l l' anti-l' is presented, which provides an
important background for Higgs boson searches in the H --> ZZ channel at the
LHC. We find that the photon contribution is important for Higgs masses below
the Z-pair threshold and that the gg-induced process yields a correction of
about 15% relative to the NLO QCD prediction for the q anti-q-induced process
when only a M(l anti-l), M(l' anti-l') > 5 GeV cut is applied.
