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A multiwavelength campaign was organized to take place between March and Julyof 2012. Excellent temporal coverage was obtained with more than 25instruments, including the MAGIC, FACT and VERITAS Cherenkov telescopes, theinstruments on board the Swift and Fermi spacecraft, and the telescopesoperated by the GASP-WEBT collaboration.  Mrk 501 showed a very high energy (VHE) gamma-ray flux above 0.2 TeV of$\sim$0.5 times the Crab Nebula flux (CU) for most of the campaign. The highestactivity occurred on 2012 June 9, when the VHE flux was $\sim$3 CU, and thepeak of the high-energy spectral component was found to be at $\sim$2 TeV. Thisstudy reports very hard X-ray spectra, and the hardest VHE spectra measured todate for Mrk 501. The fractional variability was found to increase with energy,with the highest variability occurring at VHE, and a significant correlationbetween the X-ray and VHE bands.  The unprecedentedly hard X-ray and VHE spectra measured imply that their low-and high-energy components peaked above 5 keV and 0.5 TeV, respectively, duringa large fraction of the observing campaign, and hence that Mrk 501 behaved likean extreme high-frequency- peaked blazar (EHBL) throughout the 2012 observingseason. This suggests that being an EHBL may not be a permanent characteristicof a blazar, but rather a state which may change over time. The one-zonesynchrotron self-Compton (SSC) scenario can successfully describe the segmentsof the SED where most energy is emitted, with a significant correlation betweenthe electron energy density and the VHE gamma-ray activity, suggesting thatmost of the variability may be explained by the injection of high-energyelectrons. The one-zone SSC scenario used reproduces the behaviour seen betweenthe measured X-ray and VHE gamma-ray fluxes, and predicts that the correlationbecomes stronger with increasing energy of the X-rays.

The extreme HBL behaviour of Markarian 501 during 2012