For compensating the variations in pressure of a liquid caused in particular by the piston pumps in a network, the device comprises a chamber having an inlet and an outlet for connection in series with said network and a rigid-walled hydropneumatic damping element disposed inside said chamber so that it is completely surrounded by said liquid.The device may be cleaned and sterilized without dismantling and is particularly suitable for the treatment of sterilized liquids which have to be homogenized, for example, when it is placed between the piston pump of a homogenizer and the homogenization gap.