A quasistatic theory has been constructed for predicting low frequency sheath impedance changes produced on spacecraft sounding antennas as a result of intense RF emissions by them. The theory involves calculation of time‐independent sheath profiles around an infinite cylindrical antenna in a collisionless plasma, using a numerical scheme which includes the time‐averaged repelling force on electrons due to a nonlinear effect of the RF near field of the antenna. These sheath profiles then yield values of static sheath capacitance and conductance per unit antenna length. The theory includes a more accurate electron current calculation than in the earlier treatments by the authors. Results are presented for a range of parameters applicable to spacecraft sounding conditions. In most cases, the quasistatic sheath capacitance and conductance both decrease as RF amplitude increases. At large enough RF amplitudes, the capacitance becomes almost independent of antenna potential and Debye ra