Fluorescent proteins (FPs) are widely used in two-photon microscopy as genetically encoded probes. Understanding the physical basics of their two-photon absorption (2PA) properties is therefore crucial for creation of two-photon brighter mutants. On the other hand, it can give us better insight into molecular interactions of the FP chromophore with a complex protein environment. It is known that, compared to the one-photon absorption spectrum, where the pure electronic transition is the strongest, the 2PA spectrum of a number of FPs is dominated by a vibronic transition. The physical mechanism of such intensity redistribution is not understood. Here, we present a new physical model that explains this effect through the "Herzberg-Teller"-type vibronic coupling of the difference between the permanent dipole moments in the ground and excited states (Delta mu) to the bond-length-alternating coordinate. This model also enables us to quantitatively describe a large variability of the 2PA peak intensity in a series of red FPs with the same chromophore through the interference between the "Herzberg-Teller" and Franck-Condon terms.