  We report on a theoretical study on the rise of strong peaks at the harmonics
of the cyclotron resonance in the irradiated magnetoresistance in ultraclean
two-dimensional electron systems. The motivation is the experimental
observation of a totally unexpected strong resistance peak showing up at the
second harmonic. We extend the radiation-driven electron orbit model
(previously developed to study photocurrent oscillations and zero resistance
states) to a ultraclean scenario that implies longer scattering time and longer
mean free path. Thus, when the mean free path is equivalent, in terms of
energy, to twice the cyclotron energy ($2\hbar w_{c}$), the electron behaves as
under an effective magnetic field twice the one really applied. Then, at high
radiation power and/or low temperature, a resistance spike can be observed {\it
at the second harmonic}. For even cleaner samples the energy distance could
increase to three or four times the cyclotron energy giving rise to resistance
peaks at higher harmonics (third, fourth, etc.), i.e., a resonance peak shift
to lower magnetic fields as the quality of the sample increases. Thus, by
selecting the sample mobility one automatically would select the radiation
resonance response without altering the radiation frequency.
