Abstract: The invention relative to a device for machining workpieces comprising: a chip removing, rotating tool (2) configured substantially as a hollow body including at least one cutter (4), a portion of the tool adjoining the cutter (4) being penetrated by a chip receiving opening (6) for communicating chips into a tool cavity; and an exhaust means including a stationary exhaust housing (10) configured substantially as a hollow body communicating with the cavity (8) at least in part and in connection with at least one exhaust air source; the communicating portion of the exhaust housing (10) comprising in the region of the cutter (4) a chip communicating window (26) porting into an exhaust passage (36) of the exhaust housing (10); and the exhaust passage comprising in an exhaust passage section upstream of the chip communicating window (26), relative to the exhaust direction, at least one auxiliary air infeed opening. The invention relates furthermore to a method for machining workpieces by means of one such device.