  The Crab Nebula has been observed by the HEGRA (High-Energy Gamma-Ray
Astronomy) stereoscopic system of imaging air Cherenkov telescopes (IACTs) for
a total of about 200 hrs during two observational campaigns: from September
1997 to March 1998 and from August 1998 to April 1999. The recent detailed
studies of system performance give an energy threshold and an energy resolution
for gamma-rays of 500 GeV and ~ 18%, respectively. The Crab energy spectrum was
measured with the HEGRA IACT system in a very broad energy range up to 20 TeV,
using observations at zenith angles up to 65 degrees. The Crab data can be
fitted in the energy range from 1 to 20 TeV by a simple power-law, which yields
dJg/dE = (2.79+/-0.02 +/- 0.5) 10^{-7} E^{-2.59 +/- 0.03 +/- 0.05}, ph m^{-2}
s^{-1} TeV^{-1} The Crab Nebula energy spectrum, as measured with the HEGRA
IACT system, agrees within 15% in the absolute scale and within 0.1 units in
the power law index with the latest measurements by the Whipple, CANGAROO and
CAT groups, consistent within the statistical and systematic errors quoted by
the experiments. The pure power-law spectrum of TeV gamma-rays from the Crab
Nebula constrains the physics parameters of the nebula environment as well as
the models of photon emission.
