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The first electronic states of C2O+ correlating to the first asymptotes of dissociation are presented. From accurate MRCI+Q/cc-pV5Z calculations it is shown that the electronic ground state is the X2Π state and the first excited state the a4Σ- state lying very close to the X2Π state, [image omitted] cm-1. For both states the three-dimensional PEFs are determined for displaced geometries in the range [image omitted] bohr and [image omitted] bohr about the equilibrium bond lengths and [image omitted]. The rovibronic levels up to 2200 cm-1 and J=P=7/2 are obtained for X2Π and the rovibrational levels of 4Σ- up to 5000 cm-1 and K = 4. The spin-orbit coupling between both states is investigated. [ABSTRACT FROM AUTHOR]