The observation of an astrophysical flux of high-energy neutrinos by the IceCube collaboration opened the path to multimessenger studies searching for the origin of high-energy cosmic rays since the detected neutrinos possibly originate in hadronic interactions near cosmic-ray accelerators. Although the neutrino sky map shows no indication of localized sources so far, the angular resolution of individual track-like events is sufficiently small to search for associated gamma-ray emission with Imaging Atmospheric Cherenkov Telescopes like H.E.S.S. Here we present the H.E.S.S. multi-messenger program to follow up on high-energy neutrino events. We show first results from searches for high-energy gamma-ray emission in spatial coincidence with n...