The invention relates to a hydrophobic, integrally asymmetrical hollow-fiber membrane made of a vinylidene fluoride homopolymer or copolymer, wherein the wall of the membrane has a microporous supporting layer having a sponge-like, open-pored, essentially isotropic pore structure without finger pores, the supporting layer extending across at least 90% of the wall thickness and having pores with an average diameter of less than 0.5 μm. The hollow-fiber membrane is characterized in that it has a separating layer adjacent to the supporting layer on its outer surface and that it has an outer surface with a homogeneous, uniform structure without pores, a porosity in the range from 40 to 80 vol. %, a wall thickness from 25 to 100 μm, a diameter of the lumen of the hollow-fiber membrane from 100 to 500 μm, a permeability for nitrogen of at least 25 ml/(cm2·min·bar), and an elongation at break of at least 250%. The invention further relates to a method for producing hollow-fiber membranes of this type.