Fluid-structure interaction problems arise in many different areas of engineering where the system considered or some of its components are directly in contact with a fluid. Examples are aircraft, jet engines, ships, pipelines, nuclear and chemical reactors, offshore structures, bridges, etc. In these cases, the fluid often plays an important role in determining the behavior of the structure of interest. For example, flutter could have disastrous consequences on aircraft, and resonances resulting from flow-induced vibrations could provoke structural failures in nuclear reactors, bridges and other structures subjected to a cross-flow. To prevent these potential dramatic and expensive accidents, it is necessary to seek a reliable technique for the determination of the characteristics, in particular natural frequencies, damping levels and fatigue life, of the structure in the presence of the fluid. This computation has often been accomplished in the past by relying on either a total or substantial decoupling of the fluid and structural problems, but the ever increasing emphasis on reliability, efficiency, and weight motivates the use of precise strategies for the determination of the fluid and structural behaviour. Recent efforts in this area indicate that a time-marching solution for the combined fluid and structure governing equations is computationally feasible and may provide the necessary accuracy. The present investigation essentially verities this approach and makes available a time-marching technique that fully resolves the fluid-structure interactions. As an illustration, the single airfoil flutter problem is first analysed in detail. This is followed by an investigation of the nonlinearity in the response of the airfoil. New insights thus obtained are presented and discussed. (C) 1998 Academic Press.