A fiber for thermal bonding comprising semicrystalline random copolymers of propylene, 1-hexene and optionally another .alpha.-olefin, the amount of 1-hexene being from 0.75 to less 1.52 mol % (i.e. 1.5 to less than 3 wt %) with respect to the total weight of the copolymer. The said copolymers possess a value of melt flow rate (MFR) ranging from 4 to 35 g/10 min and a molecular weight distribution, in terms of the ratio between weight average molecular weight and numeric average molecular weight ( M.sub.w/ M.sub.n), ranging from 4 to 12.