The equations describing current drive in an infinitely long plasmacylinder by means of two counter-rotating transverse magnetic fields aresolved neglecting the second and higher harmonics. The existence ofsteady-state solutions where both rotating magnetic fields (RMFs) penetrateinto the plasma much farther than the skin depth is verified. Thesesteady-state solutions admit a special case where the RMFs are of equalfrequency and magnitude, and can thus be implemented using an oscillatingtransverse magnetic field. The slip of the ion fluid with respect to theRMF is required to be extremely small (of order me/mi). Theaccessibility of these steady states from possible initial conditions isnot investigated.