Internal milling machine for machining workpieces that rotate during machining, having an internal milling cutter, with - at least one headstock with a workpiece spindle ( 2 a) rotatable in a controlled manner about an axis of rotation running in the Z-direction, - a bed with a mounting surface ( 1 a) for the at least one headstock extending in the Z- and X-directions and a lower support surface ( 1 b), - wherein the mounting surface ( 1 a) is inclined relative to the support surface ( 1 b) by a bed angle sloping downwards from the rear to the front, - at least one tool support ( 3 a) with - a Z-slide ( 4 a) movable in the Z-direction along the bed on first Z-guides ( 6 a, b), - a cross slide movable along the Z-slide ( 4 a) in one, preferably only one, direction of travel (X') transverse to the Z-direction along transverse guides ( 9 a, b), - an annular internal milling cutter which is rotatably mounted about the milling cutter axis running in the Z-direction and driveable by a milling cutter drive, - a Z-passage open in the Z-direction being formed in the Z-slide ( 4 a), characterised in that - the Z-slide ( 4 a) is configured as a portal-shaped portal slide ( 4 a) and is guided along the bed by the two lower ends of its two free-ending legs on the first Z-guides ( 6 a, b), - the direction of travel (X') of the cross slide along the portal slide ( 4 a) is inclined by an additional angle of no more than 45° relative to the X-direction. - at least one headstock with a workpiece spindle ( 2 a) rotatable in a controlled manner about an axis of rotation running in the Z-direction, - a bed with a mounting surface ( 1 a) for the at least one headstock extending in the Z- and X-directions and a lower support surface ( 1 b), - wherein the mounting surface ( 1 a) is inclined relative to the support surface ( 1 b) by a bed angle sloping downwards from the rear to the front, - at least one tool support ( 3 a) with - a Z-slide ( 4 a) movable in the Z-direction along the bed on first Z-guides ( 6 a, b), - a cross slide movable along the Z-slide ( 4 a) in one, preferably only one, direction of travel (X') transverse to the Z-direction along transverse guides ( 9 a, b), - an annular internal milling cutter which is rotatably mounted about the milling cutter axis running in the Z-direction and driveable by a milling cutter drive, - a Z-slide ( 4 a) movable in the Z-direction along the bed on first Z-guides ( 6 a, b), - a cross slide movable along the Z-slide ( 4 a) in one, preferably only one, direction of travel (X') transverse to the Z-direction along transverse guides ( 9 a, b), - an annular internal milling cutter which is rotatably mounted about the milling cutter axis running in the Z-direction and driveable by a milling cutter drive, - a Z-passage open in the Z-direction being formed in the Z-slide ( 4 a), characterised in that - the Z-slide ( 4 a) is configured as a portal-shaped portal slide ( 4 a) and is guided along the bed by the two lower ends of its two free-ending legs on the first Z-guides ( 6 a, b), - the direction of travel (X') of the cross slide along the portal slide ( 4 a) is inclined by an additional angle of no more than 45° relative to the X-direction.