TeV radiation of MRK 421 and MRK 501

The stereoscopic system of the HEGRA atmospheric Cherenkov telescopes, located on the Canary Island of La Palma, with an energy threshold of about 500 GeV, angular resolution of 5 arcmin, energy resolution ~= 20 %, and energy flux sensitivity ~= 3 times 10^{-11} erg/cm^2 s for 1 hour of observation time, has been used for 2 year (1997/1998) continuous monitoring of BL Lac objects Mrk 421 and Mrk 501. These results, combined with available simultaneous observations at other wavelengths, first of all in X-rays, provide unique information about the acceleration and radiation processes in AGN jets. Also, the time- averaged energy spectrum of Mrk 501 measured up to 25 TeV during the unprecedented (both in strength and duration) outburst of the source in 1997, provides meaningful constraints on the diffuse extragalactic background radiation at wavelengths between 1 and 50 microns.