  We continue the study of the distribution of closed geodesics on nilmanifolds
constructed from a simply connected 2-step nilpotent Lie group with a left
invariant metric and a lattice. We consider a Lie group with an associated
2-step nilpotent Lie algebra constructed from an irreducible representation of
a compact semisimple Lie algebra on a real finite dimensional vector space. We
determine sufficient conditions on the semisimple Lie algebra for the
nilmanifold to have the density of closed geodesics property for a lattice
arising from a Chevalley rational structure.
