We have considered one-dimensional organic conjugated polymeric systems to study the two-photon absorption (TPA) processes. The symmetrized density matrix renormalization group (SDMRG) method has been used to compute the low-energy photonic states and the TPA coefficients, for an extended Hubbard model. We find that the TPA coefficients diverge when the ground state of the system changes from the spin-density wave (SDW) state to the charge-density wave (CDW) state. Although in both phases the system is an insulator, the one-photon and two-photon gaps almost become equal near the transition point. The reason for the TPA coefficients to diverge is the near-degeneracy of these photonic states with strong electric dipole couplings at the transition point region. The picosecond scale nonlinear absorption processes observed in charge transfer insulating systems can be explained due to the formation of a triplet band below the lowest optically allowed state, based on our model calculations.