Super-hard γ-ray radiation spectra have been calculated. This radiation is generated near the velocity-of-light cylinder through the process of inverse-Compton scattering of relativistic electrons by thermal photons radiated by a neutron star. These calculations have been compared with observations of the Crab and Vela pulsars at 1000-GeV γ-ray energies. A correlation between γ-ray flares and those in soft (Ex ≃ lkeV) X-rays are predicted.