Our studies of the cyclotron resonance (CR) photoresistance in GaAs-based two-dimensional electron systems
(2DES) reveal an anomalously low sensitivity to the helicity of the incoming circularly polarized terahertz
radiation. We find that this anomaly is strongly intensity dependent, and the ratio of the low-temperature
photoresistance signals for the CR-active (CRA) and CR-inactive (CRI) polarities of magnetic field increases
with lowering power, but, nevertheless, remains substantially lower than expected from conventional theory
assuming interaction of the plane electromagnetic wave with the uniform 2DES. Our analysis shows that all data
can be well described by the nonlinear CR-enhanced electron gas heating in both CRA and CRI regimes. This
description, however, does not specify the source of anomalous CRI absorption that remains unclear.