The time-dependent equations describing current drive in an infinitely long plasma cylinder by means of two counter-rotating magnetic fields are solved numerically neglecting the second and higher harmonics. The accessibility of steady state solutions where both rotating magnetic fields (RMFs) penetrate into the plasma much farther than the classical skin depth, the electrons being entrained by the (−) RMF and the ions by the (+) RMF, is demonstrated. The slip of the ions with respect to the (+) RMF is required to be initially negative, with a suitable radial profile. It is also shown that the use of two counter-rotating RMFs is possible only when the frequency of the (+) RMF is larger than the electron–ion momentum-transfer collision frequency (ω+>νei).