The invention is directed to a new method for producing milled grain products such as flour, semolina, middlings, etc., wherein the material is repeatedly ground by means of rolls and sifted with the system of advanced milling. It is suggested that the material be guided again at least twice via double-roll grinding stages with sifting between the double grindings, wherein the material is sifted in each instance following the double grinding. In an especially preferred manner, a corresponding new mill with at least two double-grinding passes is preferably constructed as an 8-roll mechanism (70). In an especially preferred manner. The new mill comprises a combination of eight- (70) and four-roll mechanisms (142, 151). A screening surface which is at least 20 to 50% larger is used for the double grinding.