A linear stability analysis is performed on the base-state solution describing a pneumatically-transported system inclined at an angle theta. One of two modes was found to be dominant, depending on the tilting angle: a low-shear mode whose voidage eigenmode remains nearly symmetric from 0 degrees< theta <= theta(c), and a "boundary layer" mode for theta> theta(c), marked by significant asymmetry throughout the domain and a high level of shear inside the thin regions adjacent to the walls. The critical angle theta(c) increases with the amount of momentum and energy lost to particle-wall friction and collisions, respectively. The time-evolution of the latter mode, superimposed onto the base-state solution, reveals an alternating train of dense and dilute regions near the top of the domain, which agrees qualitatively with the development and propagation of bubbles in inclined systems observed in experiment. An analytic solution corresponding to a vertical system with a uniform base state was also derived to identify the instability mechanisms responsible for a class of non-oscillatory transverse waves which exist in both vertical and tilted particle systems. (c) 2016 American Institute of Chemical Engineers