Measurements of nonlinear losses in telecommunication fibres have been carried out with linearly polarized 532 nm 25 ps light pulses focused in optical fibres by a lens (some measurements were made also at 1064 nm). Commercial single-mode (9/125 um) and multimode (62.5/125 um) SiO2 telecommunication fibres were studied. For comparison, a plastic CKP-800 medical fibre with a core diameter of 800 um was taken. It was experimentally found that nonlinear losses become significant starting from the intensity of about 1012 W/cm2 for a single mode telecommunication fibre, of about 109 W/cm2 for a multimode telecommunication fibre, and of about 108 W/cm2 for a medical fibre. Nonlinear losses increase when the light intensity is increased (the inverse transmittance increases proportionally to the intensity within the experimental error). In the medical fibre these losses are much larger at 1064 nm. It is shown that two-photon absorption from defects is responsible for the observed nonlinear losses. We have found linear and two-photon absorption coefficients of the studied fibres and revealed that nonlinear optical losses in SiO2 telecommunication fibres are much lower than in a plastic medical fibre, which can be explained by much lower defect concentration in telecommunication fibres. Possible applications are shortly discussed.