A one-dimensional analysis of electron heating process in a weakly magnetized, inductively coupled plasma (MICP) is presented. It is found that the main difference in the heating process of a MICP from that of a usual unmagnetized ICP is in that circularly polarized wave modes can exist in the plasma. The right handed circularly polarized wave (R-wave) can propagate into the plasma and its amplitude can be enhanced by cavity resonance effect at an appropriate chamber length and external magnetic field strength. The enhanced R-wave amplitude can raise the heating efficiency significantly. It is also found that a bounce cyclotron-resonance effect can exist, which, however, is not as significant as the cavity resonance effect. (C) 1999 American Institute of Physics. [S1070-664X(99)01607-9].