A process for the continuous production of lactic acid (a first fermentation product) and of a second fermentation product selected from the group consisting of alcohols and biogas, may include starting from the milling, necessarily carried out under dry conditions, of cereals and more particularly of corn. In the context of this process, a main flow and a flow of wastes which are difficult to ferment are recovered from the milling. These two flows are treated separately but simultaneously so as to produce, by fermentation, on the one hand, lactic acid and, on the other hand, an alcohol and/or biogas.