A polymer filament comprising a polyolefin composition which comprises at least 10% by weight of one or more copolymer(s) (I) of propylene with one or more comonomers selected from ethylene, C4-C10 α-olefins and their combinations, said copolymer or copolymers (I) having MFR from 0.5 to 10 g/10 min. and containing units deriving from the said comonomers in a total amount of from 0.5 to 25% by weight with respect to the total amount of all momoner units in the copolymer, provided that, in the absence of comonomer units deriving from C6-C10 α-olefins, the amount of comonomer units deriving from ethylene or C4-C5 α-olefins or their combinations is at least 2.5% by weight.