Ab initio computations are carried out to explore the structure and stability of FNgEF₃ and FNgEF (E = Sn, Pb; Ng = Kr–Rn) compounds. They are the first reported systems to possess Ng–Sn and Ng–Pb bonds. Except for FKrEF₃, the dissociations of FNgSnF₃ and FNgEF, producing Ng and SnF₄ or EF₂, are only exergonic in nature at room temperature, whereas FNgPbF₃ has a thermochemical instability with respect to two two-body dissociation channels. However, they are kinetically stable, having positive activation barriers (ranging from 2.2 to 49.9 kcal mol⁻¹) with respect to those dissociations. The kinetic stability gradually improves in moving from the Kr to Rn analogues. The remaining possible dissociation channels for these compounds are found to be endergonic in nature. The nature of the bonding is analyzed by natural bond order, electron density, and energy decomposition analyses. Particularly, the natural population analysis reveals that they are best represented as F⁻(NgEF₃)⁺ and F⁻(NgEF)⁺. All the Xe/Rn–E bonds in FNgEF₃ and FNgEF are covalent in nature.