In this work we explain the basic ideas of a novel modelling methodology for unsteady aerodynamics based on system identification techniques. We aim to construct transfer functions (as they are often used in noise and vibration engineering) to model periodic unsteadiness. This is of direct use for the study of limit-cycle oscillations (LCO) in flutter or the vortex-induced vibration (VIV) of bluff bodies.We study a two-dimensional circular cylinder, restricted to move only in the transverse direction to the incoming flow. To describe the coupling that exists between the oscillation of the structure and the wake, we propose a model structure composed of three transfer functions. One transfer function captures all the aerodynamic forces that act on the structure during oscillation. A second transfer function translates these forces into an oscillatory motion, taking into account the structural parameters of the set up (mass, stiffness, damping). The third transfer function relates measurements from flow variables in the wake (velocity, pressure, vorticity) to the oscillation of the cylinder.We use imposed-oscillation CFD simulations to generate time series to construct the aero- dynamic transfer function. The imposed oscillation (a sinusoid, or a specific combination of sinusoids called a multisine) is used as the input signal, while the measured forces on the cylinder are the output signal.