A synthetic entry to novel dyes based on the dipyrrolonaphthyridinedione core was developed via the Heck reaction. These weakly fluorescent compounds bearing double bond linkages between the core and the peripheral units absorbed strongly in the far-red/NIR region and possessed large values of two-photon absorption (TPA) cross-sections (up to 5180 GM). Additionally, analogous dyes bearing triple bond linkages were also efficient TPA materials with relatively large two-photon absorption cross-sections (up to 2840 GM) as well as two-photon brightness (up to 1450 GM). The centrosymmetric nature of both of these families of dyes is responsible for the location of the maxima of two-photon absorption being at much higher energy than the ones corresponding to the double wavelength of the lowest-energy one-photon absorption. Theoretical calculations clarified that the enhancement of the TPA by the peripheral substitutions arose through different mechanisms depending on either the electron-donating or electron-withdrawing ability of a given substituent to the ambipolar core. The change in the electron distribution of HOMO and HOMO-1 by the push-pull effect was found to govern the strength of the lowest-energy TPA-allowed transition. Importantly, compounds from both series possessed a beneficial ratio of σ2/MW (1.6-9.8 GM/g).