To provide a fastening nut structure allowing easy execution of the mounting height adjusting operation and fastening operation of a member to be mounted, from the obverse side of the member, when such a member is to be mounted in a recess formed in the foundation part.

A projection 5b on the second nut member 5 to be fitted on a foundation bolt 3 is inserted into a through hole 2a provided in a plate member 2, which is supported from the rear side by the foundation part 5a. The mounting height of the plate member 2 relative to the foundation bolt 3 is adjusted by turning the second nut member 5 from the obverse side and varying the position relative to the foundation bolt 3. On the obverse side of the plate member 2, the first nut member 4 is fitted on a male thread portion 5d of the projection 5b, and the plate member 2 is engaged fast.