A gear, especially, bevel gear cutting machine having a workpiece cutting/deburring unit is provided to simplify the cutting/deburring procedure about a bevel gear and to improve reliability. A gear, especially, bevel gear cutting machine having a work piece cutting/deburring unit(29) comprises a workpiece carriage(5) moved in an X direction, that is, a rotation shaft line(18) of the workpiece; a stand(6) along which the workpiece carriage is adjusted in a Y direction vertical about the X direction; a tool carriage(7) adjusted in a Z direction vertical about the Y direction; and a workpiece spindle(8) rotating the workpiece carriage about a shaft line(A). The tool carriage is pivoted about a shaft line(B) disposed in parallel to a shaft line(Y), and formed with a workpiece spindle(9) rotated about a shaft line(C) extended in the Z direction.
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