Attenuation intensity dependences of 1064 nm and 532 nm picosecond pulses in multimode optical fibres produced for medical purposes by ''Anda''factory in Livani, Latvia are experimentally studied. A strong linear growth of inverse transmittance with intensity is found. The possible mechanisms of nonlinear losses are analysed and the conclusion is made that the observed effect is mainly due to the two-photon absorption involving defect levels. Strong attenuation intensity dependence can be used to make such fibre optical devices as light power limiters, optically driven light modulators and dynamic holographic frequency filters.