  Gluon-induced contributions to the associated production of a Higgs and a
Z-boson are calculated with NLO accuracy in QCD. They constitute a significant
contribution to the cross section for this process. The perturbative correction
factor (K-factor) is calculated in the limit of infinite top-quark and
vanishing bottom-quark masses. The qualitative similarity of the results to the
well-known ones for the gluon-fusion process $gg\to H$ allows to conclude that
rescaling the LO prediction by this K-factor leads to a reliable NLO result and
realistic error estimate due to missing higher-order perturbative effects. We
consider the total inclusive cross section as well as a scenario with a boosted
Higgs boson, where the Higgs boson's transverse momentum is restricted to
values ptH>200GeV. In both cases, we find large correction factors $K\approx 2$
in most of the parameter space.
