The shift to more aggressive architectures for modern aero engines has highlighted the problem of outlet guide vane (OGV) buffet. Buffeting of OGVs reduces the operability of the low pressure system and can cause structural fatigue. Therefore work to characterise, understand and mitigate this instability is of high importance. This project was motivated by static engine tests of high, off-design engine speeds where increased levels of unsteady OGV forcing were detected. OGV buffet appears to be caused by a transonic buffet aerodynamic instability, typically presenting as large, self-sustained periodic shock motion. Transonic buffet of airfoils has been studied in depth in the literature. This thesis presents the first published research on buffeting of outlet guide vanes in aero-engines and seeks to provide a greater understanding of the aerodynamic phenomenon and fluid-structure coupling mechanisms in turbomachinery environments. The literature was examined and an appropriate computational approach was selected and tested using comprehensive grid and time-step convergence studies. Steady and time-accurate sweeps of the engine operating map were conducted. These confirmed the presence of OGV buffet at the motivating engine operating conditions and established the cause as transonic buffet, featuring periodic shock motion and a following separation. The aerodynamics were examined in finer detail using a quasi-2D domain, conducting studies of the controlling parameters of inlet Mach number and incidence. The quasi-2D nature of the underlying shock oscillation was proved and a buffet boundary was mapped onto the 2D parametric space. Finally, fluid-structure coupling of OGV buffet was investigated using aeroelastic simulation. Frequency lock-in between OGV buffet and a moving blade was observed and a lock-in triangle constructed. Aeroelastic stability was quantified using an energy method calculation which showed that coupled OGV buffeting was only unstable for small excitation amplitudes, indicating limit cycle oscillation (LCO) behaviour.