A hydrostatic mounting of longitudinally displaceably arranged machine parts, which have pressure pockets for hydraulic fluid for building up a hydrostatic pressure between two machine parts, gaps connected to the pressure pockets and delimited by gap faces of the two machine parts, a drainage for the reception of hydraulic fluid flowing out from the gaps, and a seal, arranged effectively between the machine parts and surrounding the gaps, sealing against the escape of hydraulic fluid. An environment-side portion of the seal is at the same time a portion of the drainage creating a double-acting portion. The double-acting portion of the seal is formed from a material permeable to the hydraulic fluid.