Abstract: Cleaving of an optical fibre (2) is achieved by bringing a fibre cleaving blade (3) into lateral contact with such a fibre. Undue intrusion of the blade into the fibre during prior art cleaving processes can damage the fibre so as to detract from the quality of the resulting cleaved fibre end surfaces. Improvemets in the quality of the resulting end surfaces can be obtained in relation to prior art techniques by superimposing a relatively small amplitude vibratory component on a relatively steady movement of the blade towards the fibre. This can also enable the conventional use of a backing anvil at the cleaving location to be dispensed with, thereby removing danger of contamination from the anvil.