  TeV gamma-rays from the BL Lac object 1ES1959+650 have been measured during
the years 2000 and 2001 with a significance of 5.2 sigma at a value of 5.3% of
the Crab flux and in May 2002 during strong outbursts with > 23 sigma at a flux
level of up to 2.2 Crab, making 1ES1959+650 the TeV Blazar with the third best
event statistics. The deep observation of 197.4 h has been performed with the
HEGRA stereoscopic system of 5 imaging atmospheric Cherenkov telescopes (IACT
system). 1ES1959+650 is located at a redshift of z = 0.047, providing an
intermediate distance between the nearby Blazars Mkn 421 and Mkn 501, and the
much more distant object H1426+428. This makes 1ES1959+650 an important member
of the class of TeV Blazars in view of the absorption of TeV photons by the
diffuse extragalactic background radiation (DEBRA). The differential energy
spectrum of 1ES1959+650 during the flares can be fitted by a power law with a
spectral index of 2.83 +- 0.14_stat +- 0.08_sys or by a power law with an
exponential cut-off at (4.2^(+0.8)_(-0.6)_stat +- 0.9_sys) TeV and a spectral
index of 1.83 +- 0.15_stat +- 0.08_sys. The low state differential energy
spectrum obtained with lower statistics can be described by a pure power law
with a spectral index of 3.18 +- 0.17_stat +- 0.08_sys.
