  This paper presents the Extended-Soft-Core (ESC) potentials ESC08c for
baryon-baryon channels with total strangeness S=-2. The potential models for
S=-2 are based on SU(3) extensions of ESC potential models for the S=0 and S=-1
sectors, which are fitted to experimental data. Flavor SU(3)-symmetry is broken
only kinematically by the masses of the baryons and the mesons. For the S=-2
channels no experimental scattering data exist, and also the information from
hypernuclei is rather limited. Nevertheless, in the fit to the S=0 and S=-1
sectors information from the so called NAGARA event and the $\Xi$-well-depth
has been used as constraints to determine the free parameters in the
simultaneous fit of the $NN \oplus YN \oplus YY$ data. Therefore, the
potentials for the S=-2 sector are determined mainly by the NN-, YN-data, and
SU(3)-symmetry.Various properties of the potentials are illustrated by giving
results for scattering lengths, effective ranges, bound states, elastic and
inelastic phase parameters, and total cross sections. Notably is the prediction
of a bound state D$^*$ in the $\Xi N(^3S_1,I=1)$-channel with a binding energy
$B_E=1.56$ MeV. This state is deuteron-like, i.e. a member of the
$\{10^*\}$-decuplet. As for the normal deuteron $D= pn(^3S_1-^3D_1)$ the strong
tensor force is responsible for this state. The features of $\Xi$ hypernuclei
predicted by ESC08c are studied on the basis of the G-matrix approch. The
well-depth $U_\Xi= -7.0$ MeV, and the $\Xi -\Lambda\Lambda$ conversion width is
$\Gamma_\Xi^c= 4.5$ MeV.
