  Three types of rigidity theorem for orbifold elliptic genus of level N are
proved. The first type deals with the case where N is relatively prime to the
orders of all isotropy groups. If the top exterior power of the tangent bundle
is divisible by N in the Picard group of orbifold line bundles, then the
ofbifold genus of level N suitably modified has rigidity property with respect
to compact connected group actions. The second type deals with the divisibility
within the Picard group of genuine line bundles. In this case the orbifold
elliptic genus itself has rigidity property.
