Bevel gear cutting machines having multiple numerically-controllable axes, a workpiece spindle, which accommodates a bevel gear coaxially in relation to a workpiece spindle axis, and a deburring device having a deburring spindle for accommodating at least one first deburring tool. The bevel gear cutting machines may chamfer tooth edges of the bevel gear in two passes, where, in a first pass, first chamfers are provided on the tooth edges by using the first deburring tool, and, in a second pass, second chamfers are provided in the region of the first chamfers by using the first deburring tool or by using a second deburring tool in a continuous procedure, in which the bevel gear and the first or second deburring tool rotate in a coupled manner while engaged with one another.