We study the possibility that the unpulsed gamma rays in the energy ra
nge of 100 MeV-10 GeV from the direction of the Crab Nebula and pulsar
are actually emitted from a region extending to a couple of light cyl
inder radii from the pulsar instead of from the extensive nebula. In o
ur model, two pulsed photon beams from two different outer gaps cross
each other beyond the light cylinder and result in pair production. Si
nce the pitch angles of these pairs do not correlate with the local ma
gnetic field, and the typical mean free path for pair production is co
mparable to the local radius of curvature, the subsequent synchrotron
radiation and inverse Compton scattering produce unpulsed X-rays and g
amma rays, respectively.