Abstract The ability to accurately predict the forces on an aerofoil in real-time when large flow variations occur is important for a wide range of applications such as, for example, for improving the manoeuvrability and control of small aerial and underwater vehicles. Closed-form analytical formulations are only available for small flow fluctuations, which limits their applicability to gentle manoeuvres. Here we investigate large-amplitude, asymmetric pitching motions of a NACA 0018 aerofoil at a Reynolds number of $$3.2 \times 10^4$$ 3.2 × 10 4 using time-resolved force and velocity field measurements. We adapt the linear theory of Theodorsen and unsteady thin-aerofoil theory to accurately predict the lift on the aerofoil even when the flow is massively separated and the kinematics is non-sinusoidal. The accuracy of the models is remarkably good, including when large leading-edge vortices are present, but decreases when the leading and trailing edge vortices have a strong interaction. In such scenarios, however, discrepancies between the theoretically predicted and the measured lift are shown to be due to vortex lift that is calculated using the impulse theory. Based on these results, we propose a new limiting criterion for Theodorsen’s theory for a pitching aerofoil: when a coherent trailing-edge vortex is formed and it advects at a significantly slower streamwise velocity than the freestream velocity. This result is important because it extends significantly the conditions where the forces can be confidently predicted with Theodorsen’s formulation, and paves the way to the development of low-order models for high-amplitude manoeuvres characterised by massive separation. Graphic abstract