The twin-state model, previously shown to provide a simple physical rationalization for the frequency upshift (exaltation) of the Kekulé mode in benzene upon S(0) to S(1) electronic excitation, is extended to the case of the BO(2) radical and the CO(2)(+) radical cation. In the case of BO(2)/CO(2)(+), the ground and excited states are degenerate, yet the model applies to the degenerate two-state system as well. In contrast with a pseudo-Jahn-Teller model, the twin-state one can predict which frequency is exalted and also which pair of electronic states are coupled, thus explaining the specificity of the phenomenon. The frequency exaltation is a spectroscopic manifestation of the resonance between the pair of VB structures describing twin states. In analogy with the case of benzene, it is predicted that the ν(3) asymmetric stretch fundamental will be a dominant peak in the two-photon absorption spectrum of BO(2) and CO(2)(+).