Abstract: A sealing assembly for two mechanical members connected for relative rotation; a first mechanical member is fitted integrally with a substantially rigid shield, from which projects radially an annular sealing member having, on a respective first annular face, a first and a second axial sealing lip, both cooperating in sliding manner with a sealing surface of a second mechanical member; when the first annular face of the annular sealing member is subjected to a pressure substantially equal to the pressure on a second annular face, opposite the first, of the annular sealing member, only the first lip cooperates in sliding manner with the sealing surface, and the second lip mates, with no interference, with the sealing surface to permit fluid passage; conversely, when the first annular face is subjected to a pressure significantly lower than the pressure on the opposite second annular face, the annular sealing member is deformed elastically so that the second lip also cooperates in sliding manner with the sealin