The prediction of flutter and forced response at normal flow conditions has become a standard procedure during the design of compressor airfoils. But at severe off-design conditions, the flow field becomes very complex, especially during the surge blow-down phase where reversed flow conditions occur. The correct prediction of the unsteady pressures and the resulting aerodynamic excitation or damping at these conditions remains an extremely challenging task. In the first part of the paper, basic investigations for these flow conditions are presented. Aeroelastic calculations during compressor surge are shown in the second part. Experimental investigations were performed in the Annular Test Facility for non-rotating cascades at EPF Lausanne. The test cascade was exposed to flow conditions as expected during the surge blow-down phase which is characterized by large separation regions. Measurements of the steady-state flow conditions on the blade surface, at the outer wall, upstream and downstream of the cascade provided detailed information about the steady flow conditions. The cascade was then subjected to controlled vibration of the blades with constant amplitudes and inter-blade phase angles. Unsteady pressure measurements on the blade surface and at the casing wall provided information about the resulting unsteady flow conditions. Analytical CFD calculations were performed. The steady flow field was calculated using a RANS code. Based on the steady-state flow field, unsteady calculations applying a linearized code were carried out. The agreement between measurements and calculations shows that the steady flow as well as the unsteady flow phenomena can be predicted quantitatively. In addition, knowing the blade vibration mode shape, which in this case is a torsion mode, the aerodynamic damping can be determined for the corresponding flow conditions.