A threaded tubular connection that is leak-proof for internal and external successive pressure loads including a male element and a female element. At least one of the male or female elements includes a lip between the threading and the free end of the element. The lip includes a first zone with a peripheral surface turned towards the other element on which a first metallic sealing surface is disposed that can be radially interference fitted against a corresponding second metallic sealing surface disposed on the other element. The lip includes a second zone located axially between the first zone and the corresponding threading. The radial stiffness of the second zone is less than that of the first zone and that of a third zone adjacent to the second zone in the direction of the threading, and the second zone can be radially deformed by a pressure exerted thereon.