The load-following capability of a proton exchange membrane fuel cell was studied by measuring the cell voltage response to a sinusoidal current load with large amplitude and varying frequency. A mathematical model was developed, incorporating mass transport and capacitive effects as well as the membrane resistance. The model was capable of separating the faradaic and capacitive currents and predicting the observed hysteresis. At frequencies of the sinusoidal current load below 1 Hz, no appreciable hysteresis in the polarisation curve was observed. When increasing the frequency above 1 Hz, a hysteresis appeared at current densities below 0.2 A cm−2. The model related this hysteresis to capacitive effects. When using air as the cathode feed, hysteresis in the current density range 0.5 A cm−2 and higher appeared above 1 Hz compared to 100 Hz for pure oxygen. The model revealed that hysteresis observed in this current density range was caused by oxygen transport limitations.