Quantum-chemical calculations of the two-photon absorption (TPA) cross-sections are used to determine the characteristics of the electronic excited states responsible for the observed peaks in the TPA spectra of two bis-dioxaborine-substituted biphenyl derivatives. We find two distinct TPA-active states with very different TPA cross-sections: the difference is explained on the basis of electron correlation. These effects, on the one hand, lead to TPA cross-sections of up to 500 x 10(-50) cm4 s photon(-1) for the state favored by correlation; on the other hand, they limit the overall cross-sections achievable in this class of materials.