We studied nonlinear electrical transport in high-mobility 2D electron gas (2DEG) forming in modulation-doped GaAs/AlGaAs quantum wells. Transport nonlinearities induced by a pure dc electric field as well as by coexisting dc and microwave fields were studied at very high Landau level filling factors. It was observed that a pure dc electric field could induce transport nonlinearities phenomenologically similar to those previously discovered in microwave-irradiated 2DEG. New phenomena in magnetotransport emerged when a 2DEG was under the simultaneous influences of a dc electric field and a microwave field. The experimental observations were compared to the numerical simulations which were carried out based on a recently proposed theory. Generally speaking, good agreement between the experimental data and the numerical results was obtained. This suggested that the rich transport nonlinearities we have observed so far could all be coherently understood within this theoretical work.