It is well known that after one of the spatial harmonics of a boiling water reactor (BWR) is driven toward limit-cycle oscillations with a decay ratio very close to 1, the nonlinear behavior of the system starts to manifest itself, and a series of resonances appears at frequencies that are multiples of the characteristic oscillation frequency (commonly called harmonic frequencies). Several such resonances have been clearly identified during measurements in BWRs during which the system is in the unstable, limit-cycle oscillations regime. The ability to identify three and possibly four of these harmonic resonance peaks in the neutron spectra of Ringhals-1 is reported. For the measurements to be analyzed, these resonances are due to the limit-cycle oscillations not of the fundamental but of the first spatial harmonic of the neutron flux.