  Globular clusters (GCs) are established emitters of high-energy (HE, 100
MeV<E<100 GeV) \gamma-ray radiation which could originate from the cumulative
emission of the numerous millisecond pulsars (msPSRs) in the clusters' cores or
from inverse Compton (IC) scattering of relativistic leptons accelerated in the
GC environment. GCs could also constitute a new class of sources in the
very-high-energy (VHE, E>100 GeV) \gamma-ray regime, judging from the recent
detection of emission from the direction of Terzan 5 with the H.E.S.S.
telescope array.
  To search for VHE \gamma-ray sources associated with other GCs, and to put
constraints on leptonic emission models, we systematically analyzed the
observations towards 15 GCs taken with H.E.S.S. We searched for individual
sources of VHE \gamma-rays from each GC in our sample and also performed a
stacking analysis combining the data from all GCs to investigate the hypothesis
of a population of faint emitters. Assuming IC emission as the source of
emission from Terzan 5, we calculated the expected \gamma-ray flux for each of
the 15 GCs, based on their number of millisecond pulsars, their optical
brightness and the energy density of background photon fields.
  We did not detect significant emission from any of the 15 GCs. The obtained
flux upper limits allow to rule out the simple IC/msPSR scaling model for NGC
6388 and NGC 7078. The upper limits derived from the stacking analyses are
factors between 2 and 50 below the flux predicted by the simple leptonic model,
depending on the assumed source extent and the dominant target photon fields.
Therefore, Terzan 5 still remains exceptional among all GCs, as the VHE
\gamma-ray emission either arises from extra-ordinarily efficient leptonic
processes, or from a recent catastrophic event, or is even unrelated to the GC
itself.

High Energy Astrophysical Phenomena