Dynamics of an aerodynamic pendulum in steady airflow is studied using different modeling approaches: phenomenological model, where the unsteady effects are simulated using an oscillator attached to the pendulum, and modified method of discrete vortices (MMDV). It is shown that behavior of the pendulum according to the attached oscillator model agrees with data given by MMDV for a wide enough range of parameter values, and the applicability domain of the attached oscillator model is larger than that of the traditional quasi-steady approach. Stability of the "along the flow" equilibrium is studied depending on system parameters. It is shown, in particular, that this equilibrium loses its stability when the moment of inertia of the pendulum increases, if the rotation point is located in a certain range of distances upstream from the center of pressure.