  Observations of the globular clusters NGC 6388 and M 15 were carried out by
the H.E.S.S. array of Cherenkov telescopes for a live time of 27.2 and 15.2
hours respectively. No gamma-ray signal is found at the nominal target position
of NGC 6388 and M 15. In the primordial formation scenario, globular clusters
are formed in a dark matter halo and dark matter could still be present in the
baryon-dominated environment of globular clusters. This opens the possibility
of observing a dark matter self-annihilation signal. The dark matter content of
the globular clusters NGC 6388 and M 15 is modelled taking into account the
astrophysical processes that can be expected to influence the dark matter
distribution during the evolution of the globular cluster: the adiabatic
contraction of dark matter by baryons, the adiabatic growth of a black hole in
the dark matter halo and the kinetic heating of dark matter by stars. 95%
confidence level exclusion limits on the dark matter particle velocity-weighted
annihilation cross section are derived for these dark matter haloes. In the TeV
range, the limits on the velocity-weighted annihilation cross section are
derived at the 10-25 cm3 s-1 level and a few 10-24 cm3 s-1 for NGC 6388 and M
15 respectively.
