The cyclotron spin-flip excitations of a two-dimensional electron system have been investigated by inelastic light scattering (ILS). At small electron filling factors, νnot, vert, similar0.1, cyclotron spin-singlet and spin-triplet excitations have been observed, which are the magnetoplasmon and the three possible spin-flip modes that differ by their spin orientations along the axis of the quantizing magnetic field. At larger electron filling factors, ν>0.2, the electron system is fully spin-polarized. The cyclotron spin-wave (CSW) mode reenters in the ILS spectra at an electron filling factor ν>1. The CSW energy is insensitive to both the experimentally accessible in-plane momenta and the electron concentration, whereas its ILS efficiency is strongly influenced by the spin polarization of the electron system.