A so-called stepless self-tightening clamp structure having a first clamping position and a second non-clamping position in which the clamping band is under prestress of its inherent spring characteristics. To latchingly hold the clamp structure in its second position, one end of the clamping band is provided with a tongue-like extension while the other end is provided with two longitudinally extending, slot-like openings following one another by way of a constriction, whereby one of the slot-like openings is wider than the tongue-like extension and the other is slightly narrower than the tongue-like extension. One of said slot-like openings is thereby offset in the radial direction with respect to at least a part of the other slot-like opening. Additionally, to enhance the spring stiffness, the clamping band may be provided with one or more longitudinally extending reinforcing groove.