  Exchange of dominance between twin kHz quasi-periodic oscillations (QPOs)
observed in some low-mass-X-ray-binaries (LMXB) suggests the possibility of a
resonance between two oscillatory modes. We study the behaviour of the
effective gravitational potential around specific resonant radii, and estimate
the role of the higher-order terms governing the non-linear, anharmonic
forcing. We discuss the impact it has on the mode amplitude in the linear and
non--linear regimes. We also discuss a related possibility of lowering of the
neutron star mass estimates from the highest observed QPO frequencies.
