We report a detailed study of the magnetic-field-orientation dependence of the millimetre-wave magnetoconductivity of the superconductor Sr 2 RuO 4 . We find two harmonic series of cyclotron resonances. We assign the first, corresponding to a quasiparticle mass of 4.29 ± 0.05 m e , where m e is the free-electron mass, to the β Fermi-surface section. We assign the second series, which contains only odd harmonics, to cyclotron resonance of the γ Fermi-surface section, yielding a quasiparticle mass of 12.35 ± 0.20 m e . A third, single cyclotron resonance, corresponding to a quasiparticle mass of 5.60±0.03m e , is attributed to the α Fermi-surface section. In addition, we find a very strong absorption mode in the presence of a magnetic field component parallel to the quasi-two-dimensional planes of the sample. Its dependence on the orientation of the magnetic field cannot be described in the context of conventional cyclotron resonance, and the origin of this mode is not yet clear.