Abstarct: Nonlocal nonlinear axisymmetric vibration of a double-circular-nanoplate-system is considered. The two nanoplates are assumed to be bonded by an enclosing nonlinear elastic medium. Situation of this type would arise in multiple graphene sheets dispersed in nanocomposites. We use one approache to determine the nonlinear modes and natural frequencies of a clamped nanoplates are assumed to be bonded by an enclosing nonlinear elastic medium with distributed cubic nonlinearity. In this approach, we use the method of multiple scales to treat the governing partial-differential equation and boundary conditions directly. The study highlights that the smallscale effects considerably influence the transverse vibration of nonlocal double-circular-nanoplate-system(NDCNPS). The small-scale effects in NDCNPS are higher with the increasing values of nonlocal parameter for the case of synchronous modes of vibration than in the asynchronous modes. The increase of the stiffness of the coupling springs in NDCNPS reduces the small-scale effects during the asynchronous modes of vibration.