  We explain the origin of the puzzling high frequency peaks (QPOs) in the
variability power spectra of accreting neutron stars and black holes as a
non-linear 1:2 or 1:3 resonance between orbital and radial epicyclic motion.
These resonances are present because the gravitational field deviates strongly
from a Newtonian 1/r potential. Our theory agrees with the recently reported
observations of two QPOs, at 300 Hz and 450 Hz, in the black hole candidate GRO
J1655-40.
