  A {\em singular hyperbolic set} is a partially hyperbolic set with
singularities (all hyperbolic) and volume expanding central direction
\cite{MPP1}. We study connected, singular-hyperbolic, attracting sets with
dense closed orbits {\em and only one singularity}. These sets are shown to be
transitive for most $C^r$ flows in the Baire's second category sence. In
general these sets are shown to be either transitive or the union of two
homoclinic classes. In the later case we prove the existence of finitely many
homoclinic classes. Our results generalize for singular-hyperbolic systems a
well known result for hyperbolic systems in \cite{N}.
