Attenuation intensity dependences of 1064 nm and 532 nm picosecond pulses in multimode optical fibers 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 mechanism of nonlinear losses are analyzed and the conclusion is made that the observed effect is mainly due to the two-photon absorption involving defects levels. Strong attenuation intensity dependence can be used to make such fiber optical devices as light power limiters, optically driven light modulators and dynamic holographic frequency filters.