  This paper is a sequel to [He7]. There a notion of marking of isolated
hypersurface singularities was defined, and a moduli space $M_\mu^{mar}$ for
marked singularities in one $\mu$-homotopy class of isolated hypersurface
singularities was established. One can consider it as a global $\mu$-constant
stratum or as a Teichm\"uller space for singularities. It comes together with a
$\mu$-constant monodromy group $G^{mar}\subset G_Z$. Here $G_Z$ is the group of
automorphisms of a Milnor lattice which respect the Seifert form. It was
conjectured that $M_\mu^{mar}$ is connected. This is equivalent to $G^{mar}=
G_Z$. Also Torelli type conjectures were formulated. All conjectures were
proved for the simple singularities and 22 of the exceptional unimodal and
bimodal singularities. In this paper the conjectures are proved for the
remaining unimodal singularities and the remaining exceptional bimodal
singularities.
