Experiments on terahertz radiation detection with InGaAs/InAlAs field-effect transistor in quantizing magnetic field are reported. We observed oscillations of the photovoltaic signal analogous to Shubnikov-de Haas oscillations, as well as their strong enhancement at the cyclotron resonance conditions. The results are described quantitatively within the frame of a theory which takes into account a new source of nonlinearity related to the Landau quantization of the conduction band. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)