A 1-butene polymer composition comprising: a) from 10% to 90% by weight of an isotactic 1-butene polymer having the following features: i) isotactic pentad (mmmm) measured by 13C-NMR, higher than 90%; ii) melting point (TmII) higher than 90° C.; and iii) intrinsic viscosity (IV) measured in tetrahydronaphthalene (THN) at 135° C. comprised between 0.5 dl/g and 5.0 dl/g. b) from 90% to 10% by weight of a copolymer of 1-butene and at least a C8-C12 alpha-olefin derived units, containing from 0% to 10% by mole of propylene or pentene derived units, and/or containing from 0% to 5% by mole of ethylene derived units having a content of C8-C12 alpha-olefin derived units higher than 4.0% by mol and lower than 20.0% by mol; endowed with the following features: i) isotactic pentad mmmm higher than or equal to 90%; pentads (mmrr+mrrm) lower than 4 and pentad rmmr not detectable by C NMR. ii) intrinsic viscosity (IV) measured in tetrahydronaphthalene at 135° C. comprised between 0.8 and 5.0 dL/g; iii) the melting point measured by DSC (TmI) and the C8-C12 alpha-olefin content fulfil the following relationship: TmI