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The BL Lac object Mkn 501 has shown very high emission in TeV γ-rays from March to October, 1997. During this period the source was continuously monitored with the HEGRA stereoscopic system of 4 imaging air Čerenkov telescopes for a total exposure time of 110 hours. The unprecedented statistics of about 38 000 TeV photons, combined with the good energy resolution of ∼ 20% over the entire energy range and with detailed simulations of the detector response, allowed a determination of the average energy spectrum from 500 GeV to 24 TeV.
Although the γ-ray flux varied strongly with time, the daily energy spectra remained rather constant in their shape. Therefore, it is justified to derive a time averaged spectrum and thus to extend, for the first time, the spectral measurement well beyond 10 TeV. The energy resolution restricts the maximum true energy of the detected γ-rays at ∼ 18 TeV. The TeV spectrum of Mkn 501 shows a gradual steepening which could be caused by a number of physical processes, such as a limited energy range of the radiating particles, intrinsic γ-ray absorption inside the source, the Klein-Nishina effect (in the case of an inverse Compton origin of the radiation) and finally, absorption of the TeV γ-rays propagating in the intergalactic medium.