Quantum chemical ab initio calculations have been performed for linear ore-bridged binuclear transition metal complexes of the form L(5)Me(III)-O-Me(III)L(5) with Me = Ti, V, Cr. The rather bulky ligands used in the experiments have been replaced in the present theoretical study by He-like model ligands. Different basis sets and two levels of sophistication have been employed : The first step are CASSCF (complete active space SCF) and valence CI (configuration interaction) calculations in the space of the active 3d(t(2g)) orbitals at the metal ions, the second step are large-scale multireference CI calculations with all single and double excitations from all valence orbitals, including 2s, 2p at the bridging O2- ion, into the full virtual space. The CASSCF calculations can already reproduce the experimental magnetic properties of these compounds : no coupling of the spins at the two transition metal ions in the binuclear Ti(III) complex, ferromagnetic and;antiferromagnetic coupling in the V(III) and Cr(III) complexes, respectively. The mechanism of the spin coupling is the famous "superexchange", which can be described by a phenomenological exchange integral J. At the CASSCF level, the calculated values for J are too small. It needs the multireference CI to bring, the exchange integrals into reasonable agreement with experiment. The analysis of the wave functions shows that it is the balance of covalent ("neutral") and charge-transfer ("ionic") configurations that causes the differences in the magnetic behavior of the three compounds.