The presence of a kHz frequency in LMXBs has been expected from scaling laws, by analogy with the QPO phenomenon in HMXB X‐ray pulsars. Interpretation of the two kHz frequencies, observed in accreting neutron stars, in terms of non‐linear resonance in strong‐field gravity led to the prediction of twin QPOs in black hole systems, in a definite frequency ratio (such as 2/3). The imprint of a subharmonic of the 401 Hz rotation rate in the frequencies of the QPOs detected in the accreting millisecond pulsar is at once a signature of non‐linear resonance and of coupling between accretion disk modes and the neutron star spin. © 2004 American Institute of Physics