A lathe comprising: a spindle which rotates a workpiece on a spindle axis; a turret head (12h, 40) having a turret surface having a plurality of attaching positions, the plurality of attaching positions comprising a first attaching position and a second attaching position, the first attaching position and the second attaching position being adjacent to each other in a tool unit attaching direction perpendicular to a spindle axis direction extended along the spindle axis, and to the first attaching position a first tool unit being removably attached and to the second attaching position a second tool unit being removably attached; and a tool unit switching driver which switches the tool units (U01, U02) for use to machine the workpiece, wherein the second tool unit is of a shape avoiding a spindle occupying area that is capable of being occupied by the spindle during a time when the first tool unit works on the workpiece, and wherein at least one of the first tool unit and the second tool unit comprises a rotary tool unit, characterized in that when the rotary tool unit is attached to the first attaching position, a distance in the spindle axis direction from the spindle to a machining point of the second tool unit working on the workpiece is shorter than a distance in the spindle axis direction from the spindle to a rotational center of the rotary tool unit across the turret surface, wherein the second tool unit has an attaching part to be attached to the second attaching position of the turret surface and a tool holding part arranged on one side of the attaching part that is a side apart from the turret surface, wherein the tool holding part is shorter than the attaching part in length in the spindle axis direction when the second tool unit is in a position working on the workpiece, and wherein the tool holding part has a concave for receiving a shank of a tool, the concave being formed at only one end surface among two end surfaces of the tool holding part opposing each other. a spindle which rotates a workpiece on a spindle axis; a turret head (12h, 40) having a turret surface having a plurality of attaching positions, the plurality of attaching positions comprising a first attaching position and a second attaching position, the first attaching position and the second attaching position being adjacent to each other in a tool unit attaching direction perpendicular to a spindle axis direction extended along the spindle axis, and to the first attaching position a first tool unit being removably attached and to the second attaching position a second tool unit being removably attached; and a tool unit switching driver which switches the tool units (U01, U02) for use to machine the workpiece, wherein the second tool unit is of a shape avoiding a spindle occupying area that is capable of being occupied by the spindle during a time when the first tool unit works on the workpiece, and wherein at least one of the first tool unit and the second tool unit comprises a rotary tool unit, characterized in that when the rotary tool unit is attached to the first attaching position, a distance in the spindle axis direction from the spindle to a machining point of the second tool unit working on the workpiece is shorter than a distance in the spindle axis direction from the spindle to a rotational center of the rotary tool unit across the turret surface, wherein the second tool unit has an attaching part to be attached to the second attaching position of the turret surface and a tool holding part arranged on one side of the attaching part that is a side apart from the turret surface, wherein the tool holding part is shorter than the attaching part in length in the spindle axis direction when the second tool unit is in a position working on the workpiece, and wherein the tool holding part has a concave for receiving a shank of a tool, the concave being formed at only one end surface among two end surfaces of the tool holding part opposing each other.