Abstract: Provided is a double locknut assembly composed of a first nut and a second nut for fastening the first nut onto a bolt, wherein the above-mentioned first nut is formed therein with a bolt hole formed therein with a female screw thread threaded to engage with the screw thread of the bolt, the first nut having a projecting part, the outer peripheral surface of the projecting part having a truncated-conical surface on which a male screw thread is formed, the first nut being formed therein a slit so that the first nut is diametrically contractible, and the second nut is formed in the center section thereof with a bore having a truncated-conical surface formed therein with a female screw thread threaded to engage with the male screw thread on the outer peripheral surface of the projecting part of the first nut, thereby after the second nut is engaged with the first nut to a slight degree to form a one body unit, the first nut is engaged with a bolt, and thereafter the second nut is tightened to cause the first nut