We present an experimental study of electron transport in inversion layers of high-mobility Si (0 0 1) samples with occupied excited subbands. The second series of oscillations, observed in addition to the main series of Shubnikov–de Hass oscillations, is tentatively attributed to the occupation of a subband associated with the E 0′ level. Besides, a strong negative magnetoresistance and nonlinear field dependence of the Hall resistance accompany the novel oscillations at high carrier concentrations. The heating of the two-dimensional electron layers leads to suppression of the observed anomalies.