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tokens: If the synchrotron losses dominate as a radiative cooling channel, the product of the maximum attainable energy and the square root of the magnetic field strength, , can be taken as a measure of the accelerator efficiency. The extension of the electron spectrum to PeV energies in the magnetic field exceeding , tells us that in the Crab Nebula we deal with an acceleration efficiency approaching the ideal MHD limit (i.e. the strength of the accelerating electric field gets close to the strength of the magnetic field). Another important issue of the spectral modelling of the Crab Nebula is related to the so-called Crab flares – intense flashes of synchrotron radiation extending to GeV energies (Abdo et al. 2011 ; Tavani et al. 2011 ). The short variability time-scale and the distinct spectral shape of the flaring component require a magnetic field that is significantly larger than the average nebular field, , a non-ideal MHD configuration, and/or relativistic motions with a large bulk Lorentz factor (see Bühler Blandford 2014 , and references therein). Even under these extreme conditions, the Crab flares require the presence of electrons with energy exceeding a few PeV. The Crab flares are likely to be formed in a region(s) quite different from the site(s) where the steady component of radiation is produced. In both cases, the acceleration of electrons proceeds with efficiency close to or even beyond the ideal MHD limit. The tough efficiency requirement for the acceleration of the wind electrons can be significantly relaxed assuming that another component of electrons is responsible for the multi-MeV gamma-rays. This hypothesis is supported by a non-smooth transition between the spectra of the INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL ) and the Imaging Compton Telescope ( COMPTEL ). If this spectral feature is real, then it is better to reproduce the spectral structure at multi-MeV energies by invoking an additional component of electrons with a hard energy distribution (Aharonian Atoyan 1998 ). The currently available data do not exclude a significantly stronger magnetic field in the regions where this hypothetical hard distribution is localized (Aharonian Atoyan 1998 ). Therefore, the IC emission produced by electrons from the hard component could be suppressed compared with the IC radiation associated with the standard wind electron component. The synchrotron radiation alone does not allow us to infer information about the electrons and magnetic fields in this most critical – for highest energy electrons – MeV/GeV energy region. For any reasonable magnetic field, the MeV synchrotron radiation is produced by electrons of many hundreds of TeV. Therefore, the UHE gamma-rays produced by the same electrons through the IC scattering contain information that can shed light on both the electron energy distribution and the magnetic field strength. In this regard, the recently reported detection of gamma-ray fluxes above 100 TeV