We explain for the first time a long-known effect: the formation of froths, i.e. foams with lifetimes of a few seconds, in mixtures of liquids. In everyday life, this effect is generally observed in oil mixtures, such as gasoline. In contrast, pure oils do not foam because the liquid films between bubbles thin down and break up so quickly that bubbles cannot be seen with the naked eye. In some liquid mixtures, film drainage is greatly slowed down, allowing the observation of froths. We have measured this effect and we provide a quantitative explanation for it, based on the simple fact that that bulk and surface concentrations in each species slightly differ in the liquid films. These results open new perspectives for the understanding of pro and anti-foaming mechanisms in oils.