Experimental measurements of photoresistivity under terahertz (THz) radiation in low magnetic fields at conditions of cyclotron resonance (CR) in two-dimensional electron system (2DES) of GaAs/AlGaAs nanostructures are presented and discussed. We report the experimental discovery of "CR-vanishing effect" (CRV) in GaAs/AlGaAs heterostructures with high mobility as a well-defined gap on CR-line that is independent on incident THz power. Our analysis shows that the CRV may appear in systems with well correlated state of 2D electrons such as plasma waves and others. Fundamental nature of these correlated states of electrons in 2DES is discussed. Future THz detectors utilizing the new correlated states in 2DES may expand horizons for supersensitive detection in sub-THz and THz frequencies ranges.