An air-swept tube mill having at least two grinding chambers and a discharge chamber, an internal by-pass means in the last grinding chamber in communication at one end with the grinding chamber immediately preceding the last grinding chamber and at the other end, with the discharge chamber, whereby material ground in the first chamber is transferred through the by-pass directly to the discharge chamber and oversize material is transferred from the discharge chamber to the last grinding chamber for further grinding. A unique method is disclosed in which grinding of material takes place in a first grinding chamber of a tube mill and by-passed into a discharge chamber. The method further comprises feeding oversize materials from the discharge chamber into a last grinding chamber for additional grinding thereof.