The lineshape of a cyclotron resonance in a two-dimensional electron g
as is analyzed. It is shown that depending on the value of magnetic fi
eld B, two qualitatively different types of resonant absorption can ar
ise. If the resonance value of magnetic field falls within the region
where the dc Hall conductivity is quantized at low temperatures, than
the resonance, absorption lines are damped and broadened at temperatur
es T < W (W being the width of the mobility pp). With increase of the
temperature (W less-than-or-equal-to T much less than nu(eff), nu(eff)
is the frequency of electron-phonon relaxation) the amplitude of the
resonance, line grows, attains its maximum and then decreases at T gre
ater-than-or-equal-to nu(eff). In the case when the resonance absorpti
on is observed in the region off the Quantum Hall Effect steps, the te
mperature dependence of the resonance amplitude is normal.