A 1-butene polymer composition comprising: a) from 5% by weight to 95% by weight of an atactic 1-butene-based polymer, having the following features: distribution of molecular weight Mw/Mn equal to or lower than 4; rr triads, measured by 13C-NMR comprised between 5% and 50%; no enthalpy of fusion detectable at a differential scanning calorimeter (DSC); intrinsic viscosity (IV) measured in tetrahydronaphtalene (THN) at 135° C. comprised between 0.85 dl/g and 5.0 dl/g; and infrared crystallinity lower than 0.5%; b) from 5% by weight to 95% by weight of an isotactic 1-butene-based polymer having the following features: isotactic pentads (mmmm) measured by 13C-NMR, higher than 80%; melting point higher than 80° C.; and intrinsic viscosity (IV) measured in tetrahydronaphtalene (THN) at 135° C. comprised between 0.1 dl/g and 5 dl/g.