The phenomenon of bistable hysteresis in magnetic resonance of conduction electrons in solids is discussed, particularly the case of gallium oxide beta-Ga2O3. This memory effect is a consequence of the dynamic polarization of nuclei by the Overhauser effect and manifests itself by a hysteresis of the ESR line provided that particular conditions for the external (or control) and internal (or material) parameters are satisfied. The influence of all these parameters on bistability is studied in detail. it is shown that magnetic resonance of conduction electrons in solids containing nonzero nuclear spins is an intrinsically bistable phenomenon. The reasons why bistability is so strong in gallium oxide even at room temperature, compared to other identified compounds where bistability exists only at very low temperature, are discussed ill terms of electronic and crystallographic structure.