Abstract: A device for sealing an annular space between a housing having a through opening and an inner part such as a shaft rotatably mounted in the housing. The device comprises a sealing element positioned in the annular opening and sealingly connected with either the shaft or the housing and having a sealing surface adapted to cooperate with an opposing sealing surface of the shaft. A pressure fluid is supplied to a clearance between the sealing surfaces at a pressure which is higher than the pressure in the space at each side of the sealing element. The sealing surfaces have the shape the rotational surfaces inclined in relation to the axis thereof; for example, conical surfaces, and are displaceable in relation to each other so that the width of the clearance space between the sealing surfaces is at least partially determined by axial movement of the sealing surfaces in relation to each other.