A current sheet separates, beyond the closed part of the pulsar magnet
osphere, two half-spaces with oppositely directed magnetic fields. It
is shown that reconnection in this sheet may provide a source for high
-energy emission. Particles heated in the sheet just beyond the closed
part of the magnetosphere emit gamma-rays. Electron-positron pairs pr
oduced around the sheet due to gamma - gamma interaction emit in the i
nfrared and optical band. If the number density of the new-born pairs
is large enough, they affect the structure of the current sheet and it
emits also X-rays. Luminosities in the gamma-ray, X-ray and IR-optica
l bands are estimated and shown to be consistent with those observed f
rom rapidly-spinning pulsars.