We here present the H.E.S.S. follow-up of Fast Radio Bursts (FRBs), millisecond-long, very strong radio pulses of yet unknown origin. The SUPERB (SUrvey for Pulsars and Extragalactic Radio Bursts) project at the Parkes radio observatory is able to detect these enigmatic events almost in real-time which allows triggering follow-up observations covering the full electromagnetic spectrum. The H.E.S.S. gamma-ray observatory is taking active part in this endeavor. Here we focus on data taken within hours of FRB 150418, which allow us to derive the first limits on gamma-ray afterglow emission of FRBs. Based on the identification of the potential host galaxy of this burst we are able to discuss absorption effects due to the extragalactic background light (EBL) and derive intrinsic, energy dependent limits on the gamma-ray afterglow.

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