  This paper presents the Extended-Soft-Core (ESC) potentials ESC04a-d for
baryon-baryon channels with total strangeness $S=-2$. For these channels no
experimental scattering data exist, and alsothe information from hypernuclei is
very limited.The potential models for $S=-2$ are based on SU(3) extensions of
potential models for the $S=0,-1$ sectors, which are fitted to experimental
data. Flavor su(3)-symmetry is broken 'kinematically'by the masses of the
baryons and the mesons.Moreover, in ESC04a,b aldo the coupling constants are
broken, albeit in a well defined way using the $^3P_0$ quark-antiquark pair
creation model as a guidance. But the fit to the S=0 and $S=-1$ sectors
provides the necessary constraints to fix all free parameters.Therefore, the
potentials for the $S=-2$ sectors do not contain additional free parameters,
which situation is similar to the soft-core one-boson-exchange NSC97-models.
Various properties of the potentials are illustrated by giving results for
scattering lengths, bound states, phase-parameters, and total cross sections.
The features of $\Xi$-hypernuclei predicted by ESC04d are studied on the basis
of the G-matrix approach.
