Seal for sealing a circumferential gap between two machine components, one of the machine components being mounted such that it can be rotated in the axial direction relative to the other machine component, comprising: a main seal with at least one shoe for establishing a contact-free sealing action between the machine components, and with at least one spring element which supports the shoe on one of the machine components in such a way that a radial movement of the shoe is possible as a reaction to the exertion of fluid pressure on the shoe, and an auxiliary seal which seals the spring element in the axial direction, the auxiliary seal having at least two layers (14, 20) which adjoin one another in the axial direction, characterized in that - the layers (14, 20) comprise at least in each case two sheets (16, 18, 22, 24) which are positioned radially next to one another, - per layer, one of the sheets (16, 22) is stationary and the other sheet (18, 24) is mounted movably, by being fastened to the shoe, - two movable sheets (24, 30) of in each case two layers (14, 20) which adjoin one another directly having a different width, as viewed in the radial direction, the wider one of the two movable sheets being combined with a thinner, stationary sheet in order to configure the layer, and the thinner one of the two movable sheets being combined with a wider, stationary sheet in order to configure the layer, and - the wider movable sheet of the one layer overlapping in the radial direction with the wider stationary sheet of the respective other layer. a main seal with at least one shoe for establishing a contact-free sealing action between the machine components, and with at least one spring element which supports the shoe on one of the machine components in such a way that a radial movement of the shoe is possible as a reaction to the exertion of fluid pressure on the shoe, and an auxiliary seal which seals the spring element in the axial direction, the auxiliary seal having at least two layers (14, 20) which adjoin one another in the axial direction, characterized in that - the layers (14, 20) comprise at least in each case two sheets (16, 18, 22, 24) which are positioned radially next to one another, - per layer, one of the sheets (16, 22) is stationary and the other sheet (18, 24) is mounted movably, by being fastened to the shoe, - two movable sheets (24, 30) of in each case two layers (14, 20) which adjoin one another directly having a different width, as viewed in the radial direction, the wider one of the two movable sheets being combined with a thinner, stationary sheet in order to configure the layer, and the thinner one of the two movable sheets being combined with a wider, stationary sheet in order to configure the layer, and - the wider movable sheet of the one layer overlapping in the radial direction with the wider stationary sheet of the respective other layer. - the layers (14, 20) comprise at least in each case two sheets (16, 18, 22, 24) which are positioned radially next to one another, - per layer, one of the sheets (16, 22) is stationary and the other sheet (18, 24) is mounted movably, by being fastened to the shoe, - two movable sheets (24, 30) of in each case two layers (14, 20) which adjoin one another directly having a different width, as viewed in the radial direction, the wider one of the two movable sheets being combined with a thinner, stationary sheet in order to configure the layer, and the thinner one of the two movable sheets being combined with a wider, stationary sheet in order to configure the layer, and - the wider movable sheet of the one layer overlapping in the radial direction with the wider stationary sheet of the respective other layer.