The threshold intensities of the radiation required for sustaining the optical discharge waves in various silica fibres for different wavelengths of laser radiation are measured. It is shown that over a wide range of experimental conditions, the threshold intensity is determined mainly by the diameter of the mode field in the fibre. The destruction of chalcogenide and fluoride fibres upon exposure to laser radiation of power ~ 1 W is studied for the first time. The optical discharge wave is not formed in such fibres, and the destruction occurs due to thermal decomposition of the fibre material over the entire cross section of the fibre. The destruction of these fibres is characterised by much lower threshold intensities of laser radiation than in the case of silica fibres.