We present a scaling technique to analyze quantum spectra, i.e., to obtain from quantum calculations detailed information about the underlying important classical motions. The method can be applied to a general quantum system without a classical scaling property. A demonstration on the conventionally unassignable vibrational spectrum of the HO2 radical reveals remnants of classical broken tori embedded in the chaotic phase space and leads to a new assignment of spectral patterns in terms of classical Fermi resonances between the local mode motions. The scaling technique also allows to investigate the statistical properties of level spacings at fixed energies. The nearest neighbor spacing distribution of the HO2 molecule undergoes a transition from mixed phase space behavior at low energies to the Wigner distribution characteristic for chaotic systems at energies near the dissociation threshold. (C) 1997 American Institute of Physics. [S0021-9606(97)03741-0].