  We discuss properties of an exactly SO(5) symmetric ladder model. In the
strong coupling limit we demonstrate how the SO(3)-symmetric description of
spin ladders in terms of bond Bosons can be upgraded to an SO(5)-symmetric
bond-Boson model, which provides a particularly simple example for the concept
of SO(5) symmetry. Based on this representation we show that antiferro-
magnetism on one hand and superconductivity on the other hand can be understood
as condensation of either magnetic or charged Bosons into an RVB vacuum. We
identify exact eigenstates of a finite cluster with general multiplets of the
SO(5) group, and present numerical results for the single particle spectra and
spin/charge correlation functions of the SO(5)-symmetric model and identify
`fingerprints' of SO(5) symmetry in these. In particluar we show that SO(5)
symmetry implies a `generalized rigid band behavior' of the photoemission
spectrum, i.e. spectra for the doped case are rigorously identical to spectra
for spin-polarized states at half-filling. We discuss the problem of adiabatic
continuity between the SO(5) symmetric ladder and the actual t-J ladder and
demonstrate the feasibility of a `Landau mapping' between the two models.
