To provide engagement structure preventing a screw from falling off even when loosening is caused due to long-term use in an engagement mechanism for engaging two engagement parts with each other by using a parallel screw.

When a nose pad 3 serving as the second engagement part is engaged with a pedestal 4 serving as the first engagement part by using the parallel screw 6, the parallel screw 6 is inserted from a first through hole 41 of the pedestal 4, advances through a third through hole 33 of an oscillation bearing part 31 of the nose pad 3 while a male screw groove 65 provided on a tip end part 64 is screwed into a female screw groove 44 provided on a second through hole 42 of the pedestal 4, and is screwed until the tip end part 64 completely protrudes outward from the second through hole 42. In that state, since engagement of the male screw groove 65 with the female screw groove 44 is released, the parallel screw 6 is prevented from falling off from the pedestal 4 by rotating in a loosening direction.