Nonlinear quantum transport phenomena caused by the singular nature of a two-dimensional (2D) electron gas in a magnetic field is studied for a nondegenerate system like the surface electrons (SE) on liquid helium. A strong decrease in the longitudinal magnetoconductivity is shown to occur without heating of the electron system. The results obtained can be used for complementary experimental study of the single-electron and many-body properties of a 2D electron liquid in quantizing magnetic fields.