  Mrk 501 has been in a state of very high flux in X-rays and VHE gamma-rays
during 1997. In July 1997 near its hitherto maximum X-ray brightness intense
multifrequency observations of Mrk 501 have been performed at radio, near
infrared, optical, X-ray, and VHE gamma-ray frequencies.
  Here we report on Rossi X-ray Timing Explorer (RXTE) observations carried out
in 1997 between July 11 and July 16. The X-ray spectrum has been well detected
up to 100 keV and is best described by a broken power law with spectral indices
alpha1=0.70 and alpha2=0.94 below and above the break energy 5.8 keV.
  The X-ray flux from Mrk 501 declined and flared by about 30% within about 3
days each, showing an unusual anti-correlation between flux and spectral
hardening of both power law components. The break energy remained constant.
  The observed broad band and X-ray spectra confirm recent observations, that
the synchrotron component in Mrk 501 can extend up to energies of 100 keV with
the maximum power being emitted at hard X-rays. On longer time-scales the
cut-off frequency of the synchrotron spectrum changes by more than two orders
of magnitude.
