- A 3-min outburst of very-high energy (VHE) quanta, E > 1012 eV, was recently detected from the X-ray pulsar Hercules X-1 (ref. 1). The outburst occurred at a time during the 35-day X-ray modulation that is associated with X-ray turn-on. Temporal analysis of the outburst showed the same 1.24-s modulation that is observed at X-ray energies. Subsequent monitoring of the system at ultra-high energies (UHE) by the Fly's Eye2 yielded evidence for a 40-min outburst of quanta with energies E>1×l014TeV. This UHE outburst also exhibited a 1.24-s modulation. Here we assume the quanta to be γ-rays and show how the interaction of these UHE particles with a precessing accretion disk can explain the observed γ-ray ‘light’ curve. We also discuss the possibility that the emitting UHE particles are accelerated by shocks in an accretion flow as well as the constraints that can be placed on the acceleration mechanism.