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To lower the lightning impulse withstand voltage of gas insulated switchgear (GIS) while maintaining the high reliability of its insulation performance, it is important to define in an organized way the insulation characteristics for non-standard lightning impulse voltage waveforms that represent actual surge waveforms in the field and compare them with the characteristics for the standard lightning impulse waveform quantitatively. In the previous work, the dielectric breakdown voltage - time characteristics were measured under several different conditions on the quasi-uniform SF6 gas gap and partly the cone-shaped insulating spacers that represent an insulation element of GIS for six kinds of non-standard lightning impulse waveforms associated with lightning surges and disconnector switching surges. This paper, describes detailed examination in non-uniform electric field, and the pattern in which a disconnector switching surges are superposed on residual DC elements generated through the operation of disconnectors (bias voltages). This is intended to simulate more severe conditions in an actual system. Consequently, it was found that the presence of a bias voltage in the nonuniform electric field resulted in lower breakdown voltage values for single-frequency oscillation waveforms both in the positive and negative polarities. However, the breakdown voltage values under positive-polarity waveforms posing more severe insulation conditions were higher than the ones under the standard lightning impulse waveforms. Despite the presence of a bias voltage, it was possible to evaluate these breakdown voltage values in the positive polarity using the concept of a duration examined in the past.