While there is a body of experimental data concerning dimers formed by an aromatic molecule and its radical cation, information on the corresponding dimer radical anions (DRAs) is scarce. In this work, evidence for the formation of the DRAs of decafluorobiphenyl and 4-aminononafluorobiphenyl has been obtained by the optically detected electron paramagnetic resonance and the time-resolved magnetic field effect techniques. Theoretical investigation (DFT B3LYP-D3/6-31+G*) of these DRAs and the DRAs of octafluoronaphtalene and 1,2,4,5-tetrafluorobenzene previously detected by Werst has been undertaken to gain greater insight into the structure of the polyfluoroarene DRAs. Without substituents different from a fluorine atom, an extra electron is evenly delocalized over two fragments; the bonding interaction is π stacking. On the potential energy surfaces (PES), there are two minima of nearly equal energy corresponding to the structures of perfect and parallel displaced sandwiches. Such a PES structure is due to a conical intersection between two electronic states of different symmetry. The DRA of 4-aminononafluorobiphenyl is an ion-molecular associate stabilized by electrostatic interactions involving NH2 groups. The complex cyclic structure of the PES of this DRA suits the successive electron transfers between the dimer fragments. The calculated hyperfine coupling constants averaged over the PES minima agree well with the experimental ones.