The possible existence of two stable states connected by a single electron transfer has been studied in two different cases: (i) the cation of a molecular dimer (A2)+, which is necessarily symmetrical (with a delocalized hole) at short enough intermolecular distances, and symmetry-broken (with a localized hole) at long intermolecular distances. The symmetry-breaking appears as a bifurcation, as shown through model studies of the (H2⋯H2)+ dimer. It takes place when the relaxation energy of the localized forms prevails over the left-right hole-delocalization resonance energy. At the Hartree-Fock (HF) level with a rectangular geometry, the conflict takes the form of an instability of the symmetry-adapted solution for intermolecular distances larger than a critical value; the behavior is exactly the same for the exact solutions of the electronic Born-Oppenheimer Hamiltonian with respect to the rectangular ↔ trapezoid geometric distortion, so that the HF instability may be looked at as a metaphor (involving electronic relaxation) of a more physical phenomenon involving the nuclear relaxation. (ii) the donor-acceptor (DA) complexes and the DA ↔ D+A- transition in which the most stable structure is ionic at short intermolecular distance and neutral at large intermolecular distance. The problem is analyzed as the matching of two valleys, and two solutions are possible: either an oblique passage from one channel to the other or the coexistence in a certain domain of intersystem distances of two parallel valleys of different heights and slopes which are separated by a saddle point. This is a case of bistability (for fixed intersystem distance). The problem is again analyzed first at the HF level, regarding the electronic relaxation vs electron delocalization conflict, and it is shown that for the heteropolar molecules one may have either a classical instability behavior (FH molecule) or a bistability behavior: in LiF the neutral UHF and ionic HF solutions are both stable between 6 and 46 bohr! The same "bistability" behavior may exist on the exact potential energy surface, as shown for the Li2 + F problem. A final discussion points out the requirements to be satisfied in building bistable DA complexes, and suggestions are made accordingly. © 1992 American Chemical Society.