Unipotent representations attached to spherical nilpotent orbits

A coadjoint nilpotent orbit O of a complex semisimple Lie group G is said t o be spherical if it contains an open orbit of a Borel subgroup. We determi ne when and how to attach unitary representations to such an orbit for the real orthogonal and symplectic groups. Our results actually extend to a lar ger class of nilpotent coadjoint orbits.