  The superdeformation and hyperdeformation in $^{108}$Cd have been studied for
the first time within the framework of the fully self-consistent cranked mean
field theory, namely, cranked relativistic mean field theory. The structure of
observed superdeformed bands 1 and 2 have been analyzed in detail. The bumps
seen in their dynamic moments of inertia are explained as arising from unpaired
band crossings. This is contrary to an explanation given earlier within the
framework of projected shell model. It was also concluded that this nucleus is
not doubly magic SD nucleus.
