An assembly for producing a threaded connection includes first and second tubular components with an axis of revolution and each provided at one end with at least first, second, and third continuous threaded zones provided in succession on the same helix on the outer or inner peripheral surface of the component depending on whether the threaded end is male or female. The components are capable of cooperating together upon makeup. At least one of the first, second, or third threaded zones has a variable width thread profile and is self-locking. The ends respectively finish in a free terminal surface. Each of the ends is free of a specific abutment surface. At least one sealing surface is provided between each of the adjacent threaded zones in order to cooperate in a sealed interference fit with a sealing surface provided on the corresponding end when the connection is made up.