A threaded tubular connection which is leak-proof for internal and external successive pressure loads with comprises a male element (11) and a female element (12). At least one of the male or female elements (11, 12) comprises a lip (14, 16) between the threading (13, 15) and the free end of the element (17, 18). The lip (16) comprises a first zone (20) with a peripheral surface turned towards the other element (11) on which a first metallic sealing surface (22) is disposed which can be radially interference fitted against a corresponding second metallic sealing surface (23) disposed on the other element (11). The lip (16) has a second zone (21) located axially between said first zone (20) and the corresponding threading (15). The radial stiffness of the second zone (21) is less than that of the first zone (20) and that of a third zone adjacent to the second zone (21) in the direction of the threading (15), and zone (21) can be radially deformed by a pressure which is exerted thereon.