We present a systematic investigation of the microwave absorption for two-dimensional electron layers on thin helium films and in the presence of a cyclotron resonance ͑CR͒ magnetic field. To explain the measured data, a recently proposed two-fraction structure of the electron system is used and here described in detail. Hereby the problem of substrate roughness, usually always present for electrons on thin helium films, is taken into account and it turns out to be an important parameter.

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... this model the general structure of the microwave absorption becomes understandable and the fraction of localized and free electrons can be precisely determined. The details of the observed asymmetry and shift of the CR line shape are discussed.