Synthetic dyes having high photostability on hydrophobic fibers such as poly(ethylene terephthalate) (PET) are of interest for use on textile substrates for outdoor applications. While much is known about photostable dyes developed for PET in the 1980s, owing to their viability for use in automobile interiors, little has been published on currently viable photostable disperse dyes. As part of an effort to help fill this void and to facilitate future photostable disperse dye design, the present study involved the use of experimental measurements and modelling studies to help characterize the molecular structures of commercially viable dyes for producing photostable colors on PET fibers, beginning with a pair of blue dyes. With the aid of HR-MS, 500 MHz 1H NMR, and X-ray crystallography, it was established that the two dyes are structural isomers having 1,5-(OH)2-anthraquinone (AQ) and 1,8-(OH)2-AQ base structures. It is proposed that the photostability of these dyes arises from the presence of multiple OH/NH groups ortho to the AQ CO groups which enables them to dissipate excited state energy through intramolecular proton transfer. Further, using DFT-based molecular modelling studies, it was shown that the dye having the 1,5-(OH)2-AQ base structure has a lower ESOP than the isomeric dye having the 1,8-(OH)2-AQ base structure. Similarly, results from calculating Frontier HOMO and LUMO isosurfaces indicated that the LUMO lobes of the latter dye are larger, suggesting that this dye undergoes excitation faster than the 1,5-(OH)2-AQ isomer.