One of the limitations of the Arrhenius definition is its reliance on water solutions. Edward Curtis Franklin studied the acid–base reactions in liquid ammonia in 1905 and pointed out the similarities to the water-based Arrhenius theory. Albert F.O. Germann, working with liquid phosgene, , formulated the solvent-based theory in 1925, thereby generalizing the Arrhenius definition to cover aprotic solvents.
Germann pointed out that in many solutions, there are ions in equilibrium with the neutral solvent molecules:
* solvonium ions: a generic name for positive ions. These are also sometimes called solvo-acids; when protonated solvent, they are lyonium ions.  
* solvate ions: a generic name for negative ions.  These are also sometimes called solve-bases; when deprotonated solvent, they are lyate ions.  
For example, water and ammonia undergo such dissociation into hydronium and hydroxide, and ammonium and amide, respectively:
Some aprotic systems also undergo such dissociation, such as dinitrogen tetroxide into nitrosonium and nitrate, antimony trichloride into dichloroantimonium and tetrachloroantimonate, and phosgene into chlorocarboxonium and chloride:
A solute that causes an increase in the concentration of the solvonium ions and a decrease in the concentration of solvate ions is defined as an acid. A solute that causes an increase in the concentration of the solvate ions and a decrease in the concentration of the solvonium ions is defined as a base.
Thus, in liquid ammonia,  (supplying ) is a strong base, and  (supplying ) is a strong acid. In liquid sulfur dioxide (), thionyl compounds (supplying ) behave as acids, and sulfites (supplying ) behave as bases.
The non-aqueous acid–base reactions in liquid ammonia are similar to the reactions in water:
Nitric acid can be a base in liquid sulfuric acid:
The unique strength of this definition shows in describing the reactions in aprotic solvents; for example, in liquid :
Because the solvent system definition depends on the solute as well as on the solvent itself, a particular solute can be either an acid or a base depending on the choice of the solvent:  is a strong acid in water, a weak acid in acetic acid, and a weak base in fluorosulfonic acid; this characteristic of the theory has been seen as both a strength and a weakness, because some substances (such as  and ) have been seen to be acidic or basic on their own right. On the other hand, solvent system theory has been criticized as being too general to be useful. Also, it has been thought that there is something intrinsically acidic about hydrogen compounds, a property not shared by non-hydrogenic solvonium salts.