  The observations of gamma-ray emission from pulsars with the Fermi-LAT
detector and the detection of the Crab pulsar with the VERITAS array of
Cherenkov telescopes at energies above 100 GeV make it unlikely that curvature
radiation is the main source of photons above GeV energies in the Crab and many
other pulsars. We outline a model in which the broad UV-X-ray component and the
very high energy \gamma-ray emission of pulsars are explained within the
Synchrotron-Self-Compton (SSC) framework. We argue that the bulk of the
observed radiation is generated by the secondary plasma, which is produced in
cascades in the outer gaps of the magnetosphere. We find that the
inverse-Compton (IC) scattering occurs in the Klein-Nishina regime, which
favors synchrotron photons in the UV band as target field for the scattering
process. The primary beam is accelerated in a modest electric field, with a
field strength that is of the order of a few percent of the magnetic field near
the light cylinder. Overall, in the Klein-Nishina regime of the IC scattering
the particle distribution in the gap does not evolve towards a stationary
distribution and thus is intrinsically time-dependent. We point out that in a
radiation reaction-limited regime of particle acceleration the gamma-ray
luminosity L_{\gamma} scales linearly with the pulsar spin-down power \dot{E},
L_\gamma ~ \dot{E}, and not proportional to \sqrt{\dot{E}} as expected from
potential-limited acceleration.
