Particle acceleration and synchrotron emission in Mrk 501

Mrk 501 became very active in 1997. The cut-off frequency of the synchrotro n emission increased by two orders of magnitude during an extensive flare, lasting several months. The increase in hard X-ray flux is accompanied by an increase in TeV emissi on. We have carried out several multi-frequency campaigns in 1997 and 1998, involving observations of the X-ray spectrum with SAS and XTE, as well as low-frequency monitoring during epochs of intense TeV observations. Here we report on a campaign carried out in July 1997. We find the X-ray spectra to be composed of several components with very di fferent cut-off energies and different variability patterns. We model the v ariation of the synchrotron spectra with several components, the evolution of which is tightly constrained by the wide-band coverage of the SED and th e dense temporal coverage. The temporal characteristics indicate that acceleration time-scales are sho rt but longer than cooling time-scales throughout the entire regime of phot on energies covered in this study. We will present a consistent modeling of the synchrotron spectra up to the highest energies and provide important c onstraints on the acceleration mechanisms.