A method is provided for cutting a glass duct, whereby the glass duct can be cut off completely straight. In this method, the coating layer is first cut through all round at the axial location of the fiber where the fiber is to be notched before the notching and subsequent breaking off of the glass duct. To enable the use of this method for glass ducts of varying diameters, the glass duct can be retained in a fixed position during cutting, while a cutting member, as well as a counterpressure surface for the cutting member, are moved all round the glass duct. Because glass ducts of a relatively small diameter are pressed further sidewards by the cutting member than glass ducts of greater diameter, this method effectively limits this sidewards displacement to prevent the glass ducts from breaking in an unintended manner.