A nonlinear aeroelastic methodology for inflatable/ballute type structures has been successfully developed for, a heuristic case: a 2D membrane-on-wedge model, and an axisymmetric modeled ballute system (MBS), under hypersonic/supersonic shock waves. Specifically, the nonlinear structural ROM methodology ELSTEP/FAT is extended and validated (based on MSC.Nastran FEM model) to the membrane-on-wedge model and the axisymmetric MBS. The time-accurate GasKinetic BGKX methodology has been developed as the key aerodynamic solver. It has great advantages over current continuum CFD solvers with its solution robustness, one-step computation of pressure and heat flux, and broad range of Knudsen number for hypersonic applications. Nonlinear aerodynamic static deformations at various altitudes have been obtained through a tight coupling between the nonlinear structural ROM and the direct BGKX aerodynamic solver. An efficient aerodynamic ROM has been developed for the undeformed/deformed mean 2D/axisymmetric configurations using a system identification technique with staggered modal inputs. The aerodynamic ROM solutions are found to closely match the direct BGK solutions. ROM-ROM time-domain dynamic aeroelastic analyses reveal significant differences between analyses carried out around the undeformed configuration and around the deformed one. In particular, a decrease in altitude will increase the static deformations which lead to a stiffer behavior with respect to additional small perturbations. Accordingly, a decrease in altitude induces an increased stability, in contrary to aeroelastic solutions for the undeformed configuration. This fundamental observation demonstrates the need to perform tightly coupled steady aeroelastic analyses prior to any stability analysis.