A density functional theory study is performed to determine the stability and bonding in the neon dimer inside the B30N30 fullerene cage, the fluxional B40 cage, and within non-fluxional cages such as B12N12 and C60. The nature of bonding in the Ne2 encapsulated B40 is compared with the that in other cages in an attempt to determine whether any possible alterations are brought about by the dynamical nature of the host cage apart from the associated confinement effects. The bonding analysis includes the natural bond order (NBO), Bader’s Atoms-in-Molecules electron density analysis (AIM), and energy decomposition analysis (EDA), revealing the non-covalent nature of the interactions between the Ne atoms and that between the Ne and the cage atoms. The formation of all the Ne2@cage systems is thermochemically unfavourable, the least being that for the B30N30 cage, which can easily be made favourable at lower temperatures. The Ne-Ne distance is lowest in the smallest cage and increases as the cage size increase due to steric relaxation experienced by the dimer. The dynamical picture of the systems is investigated by performing ab initio molecular dynamics simulations using the atom-centred density matrix propagation (ADMP) technique, which shows the nature of the movement of the dimer inside the cages, and by the fact that since it moves as a single entity, a weak bonding force holds them together, apart from their proven kinetic stability.