This paper studies the normal and abnormal regimes of a weak-current rf discharge in ammonia, nitrogen, hydrogen and N 2 O for the rf electric field frequencies of 13.56 and 27.12 MHz. We reveal that only the abnormal regime of burning is observed at low pressures when the current growth is accompanied by an rf voltage increase while the surface of the electrodes is completely covered with the discharge. The normal regime occurs at higher gas pressures when the current growth is due to the increase in the surface area occupied by the discharge on the electrodes. The discharge burns in the abnormal mode after the surface of the electrodes is completely covered with the discharge. We demonstrate that the normal current density is directly proportional to the gas pressure and it depends approximately on the square of the rf electric field frequency. We present an analytical model for two limiting cases: constant free path length and constant mobility of positive ions furnishing a satisfactory description of the experimental data.