A gear processing machine, in particular a gear hard finishing machine, comprising: a) a machine frame, b) a spindle slide having a first spindle, which comprises a first spindle housing and a first spindle shaft, wherein the first spindle shaft is arranged in the first spindle housing such that it can be rotated around a first spindle axis and has a free end for receiving a workpiece or a tool, and c) a second spindle having a second spindle housing and a second spindle shaft, wherein the second spindle shaft is arranged in the second spindle housing such that it can be rotated around a second spindle axis in order to receive a tool or workpiece, d) wherein at least one wall of the machine frame forms a part of the shell of a closable working space in which the workpiece is able to be machined and which can be closed off in order to prevent any removed material, machining liquid and/or machining mist from escaping from the working space into other machine regions or to the outside, e) and the spindle slide is arranged on the machine frame such that it can be moved in the direction of the first spindle axis, f) and the closable working space encloses the free end of the first spindle shaft and at least partially encloses the second spindle shaft, characterised in that g) the gear processing machine comprises a bellows which is firmly connected to the spindle slide on a first side and to the at least one wall of the machine frame on a second side, h) wherein the bellows delimits the closable working space in at least one place such that a part of the spindle slide is located permanently outside of the working space, and i) wherein the bellows is capable, by expanding or contracting, of accommodating any relative movement in the direction of the first spindle axis between the spindle slide and the machine frame. a) a machine frame, b) a spindle slide having a first spindle, which comprises a first spindle housing and a first spindle shaft, wherein the first spindle shaft is arranged in the first spindle housing such that it can be rotated around a first spindle axis and has a free end for receiving a workpiece or a tool, and c) a second spindle having a second spindle housing and a second spindle shaft, wherein the second spindle shaft is arranged in the second spindle housing such that it can be rotated around a second spindle axis in order to receive a tool or workpiece, d) wherein at least one wall of the machine frame forms a part of the shell of a closable working space in which the workpiece is able to be machined and which can be closed off in order to prevent any removed material, machining liquid and/or machining mist from escaping from the working space into other machine regions or to the outside, e) and the spindle slide is arranged on the machine frame such that it can be moved in the direction of the first spindle axis, f) and the closable working space encloses the free end of the first spindle shaft and at least partially encloses the second spindle shaft, g) the gear processing machine comprises a bellows which is firmly connected to the spindle slide on a first side and to the at least one wall of the machine frame on a second side, h) wherein the bellows delimits the closable working space in at least one place such that a part of the spindle slide is located permanently outside of the working space, and i) wherein the bellows is capable, by expanding or contracting, of accommodating any relative movement in the direction of the first spindle axis between the spindle slide and the machine frame.