We have grown n-type modulation-doped Cd(Mn)Te/(Cd,Mg)Te single quantum wells (SQWs) by molecular beam epitaxy (MBE). The properties of two-dimensional electron gas in obtained samples are the following, the sheet carrier density was about 3 x 10(11) cm(-2) and the Hall mobility of CdTe SQW was 6 x 10(4) cm(2)/V s at 2 K, but that of Cd1-xMnxTe SQWs with x = 0.01-0.03 was decreased by about one order of magnitude. In the magnetotransport measurements up to 14 T at 2 K, typical features of the integer quantum Hall effect (IQHE), that is, zeros of magnetoresistance (MR) and quantized plateaux of the Hall resistance, were observed in a CdTe SQW sample. In Cd1-xMnxTe SQWs, on the other hand, the oscillation of MR associated with the transition between spin-split levels was observed at lower fields than the non-magnetic CdTe SQW, which reflected enhanced Zeeman splitting due to the exchange interaction with Mn2+ spins. Further, large positive and negative MR at low fields was observed in Cd1-xMnxTe SQWs, both of which are also attributed to the exchange-enhanced spin splitting. (C) 2001 Elsevier Science B.V. All rights reserved.