The invention is based on a damper element for damping a pulsating fluid flow particularly for smoothing out and reducing pressure fluctuations arising in fuel supply systems for internal combustion engines of motor vehicles having at least one elastic, non-metallic damper diaphragm. A damper element is already known which in order to smooth out and reduce pressure fluctuations communicates with the pressurized fuel of a fuel injection system and has a fabric diaphragm as its damper member. The fabric diaphragm is not absolutely impermeable to fuel, however, so that over a relatively long period in operation, more and more fuel diffuses through the fabric diaphragm into the damper chamber located behind it, the damper chamber being unventilated for safety reasons. The fuel collecting in the damper chamber impairs the damping effect more and more with time, until the damping effect actually ceases.