Abstract: An anti-loosening nut assembly is composed of an upper nut 3 and a lower nut 2 that engage with each other in an eccentric manner to afford the so-called ‘wedging’ effect of surely inhibiting them from loosening themselves. The upper nut 3 has one or more lateral lugs to be brought into contact with the lower end of a fastening tool such as a spanner. The lug or lugs 3b protrudes or protrude from the outer peripheral portion or portions of the upper nut 3 for the purpose of visual detection of rotation angle of this nut.