X-ray and gamma-ray emission from pulsar magnetospheres

For polar-cap models based on electromagnetic cascades induced by curvature radiation of beam particles we calculate broad-band high-energy spectra of pulsed emission expected for classical (similar to 10(12) G) and milliseco nd pulsars (similar to 10(9) G). The spectra are a superposition of curvatu re and synchrotron radiation components and most of their detailed features depend significantly on the magnetic field strength. The relations of expe cted pulsed luminosity L-X (between 0.1 keV and 10 keV) as well as L-gamma (above 100 keV) to the spin-down luminosity Lsd are presented. We conclude that spectral properties and fluxes of pulsed non-thermal X-ray emission of some objects, like the Crab or the millisecond pulsar B1821-24, pose a cha llenge to the polar-cap models based on curvature and synchrotron radiation alone. On the other hand, such models may offer an explanation for the cas e of B1706-44.