  We compute the QCD corrections at next-to-leading order for the process $gg
\rightarrow ZH$, including both the virtual two-loop terms and real-emission
contributions. The two-loop box diagrams in the virtual corrections are
approximated analytically over the complete phase space, combining the results
of an expansion in the limit of small transverse momentum and an expansion in
the regime of high energy. We obtain both inclusive and differential results
for the cross section. We find that the NLO QCD corrections are of the same
size as the LO contribution up to $ZH$ invariant masses close to 1 TeV, but
they increase significantly when higher energies are considered, due to a class
of real-emission diagrams in which the $Z$ boson is radiated from an open quark
line. Finally, we estimate the uncertainty due to the renormalization scheme
used for the top-quark mass both on the total and differential cross section.
