A method of treating sepsis comprising treating a patient with sepsis by passing a body fluid of the patient through a device for removing both bacterial lipopolysaccharides lipoteichoic acids from a body fluid, said device comprising a housing that can be incorporated into the perfusion system, a chemically modified hollow fiber material that is suitable for the collective removal of both bacterial lipoteichoic acids and lipopolysaceharides in the housing, the device being arranged such that the blood or plasma entering through a first opening of the housing must pass through the hollow fiber material before it leaves through a second opening of the housing and is directed to the rest of the perfusion system, wherein said hollow fiber material comprises at least one polymer selected from the group consisting of polyamide, polysulfone, polyether, polyethylene, polypropylene, polyester, derivatives and mixtures thereof, wherein said hollow fiber material has tentacles comprising an anion exchange group polymerized thereon by graft polymerization, wherein the anion exchange group comprises at least one of the group consisting of a synthetic polycationic chain, a semisynthetic polycationic chain and a natural polycationic chain, wherein said synthetic, semisynthetic and natural polycationic chains are linear or branched and wherein said device has a dead volume <150 ml.