The two-photon absorption (2PA) properties are investigated for two series of organic, π-conjugated, fused-ring, quadrupolar A-π-D-π-A chromophores of the type originally developed as nonfullerene acceptors for organic photovoltaics. These molecules are found to exhibit large nondegenerate two-photon absorption (ND2PA) cross-sections (ca. 6-27 × 103 GM) in the near-infrared (NIR). In the first series, involving molecules of varying core size, ND2PA spectra and cross-sections characterized by femtosecond ND2PA spectroscopy in chloroform solutions reveal that increases in core size, and thus conjugation length, leads to substantially red-shifted and enhanced 2PA. In a second series, variation of the strength of the terminal acceptor (A) with constant core size (seven rings, indacene-based) led to less dramatic variation in the 2PA properties. Among the two core types studied, compounds in which the donor has a thieno[3,2-b]thiophene center demonstrate larger 2PA cross-sections than their indacene-centered counterparts, due to the greater electron-richness of their cores amplifying intramolecular charge transfer. Excited-state absorption (ESA) contributions to nonlinear absorption measured by open-aperture Z-scans are deduced for some of the compounds by analyzing the spectral overlap between 2PA bands and NIR ESA transitions obtained by ND2PA and transient absorption measurements, respectively. ESA cross-sections extracted from transient absorption and irradiance-dependent open-aperture Z-scans are in reasonable agreement, and their moderate magnitudes (ca. 10-21 m2) suggest that, although ESA contributions are non-negligible, the effective response is predominantly instantaneous 2PA.