The set of important properties of polymers necessary for their use as fuel cell membranes, such as film-forming properties, stability in acidic aqueous media, thermal stability, proton conductivity, is determined by their chemical structure, which provides not only basic and fragmentary mobility of the polymer chain but also complex supramolecular structural features (in particular, phase separation). The effect of the chemical structure of aromatic polyimide sulfonic acids, containing a fragment of 4,4′-diamino[1,1′-biphenyl]-2,2′-disulfonic acid (BDSA), on their membrane-forming properties is discussed, as well as the membrane stability under the conditions of a hydrogen-air fuel cell. The research is aimed at investigating sulfonated polyimides based on the commercially available rigid monomer - BDSA and flexible dianhydrides with an electron donor in their structure. As a model for this study, two aromatic anhydrides with flexible -O- bonds were chosen for investigating the potential of corresponding polyimide films in application to proton exchange membranes. The synthesized sulfonic acid polyimide BDSA-SPI-4(H) is of interest as a proton-conducting membrane polymer for direct energy conversion electrochemical devices and has shown to be a promising material for this group of devices. It is suggested that the presence of the flexible electron donor bonds in the structure of dianhydride should increase the stability of the membranes prepared from BDSA. The properties of polyimide sulfonic acids from the aforementioned diamine and dianhydrides of different fragmentary flexibility implemented in this work could help the understanding of the connection between chemical structure and properties of the material in application to proton exchange membranes development.