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To lower the insulation specifications (specifically, the lightning impulse withstand voltage) of a gas insulated switchgear (GIS) and thus cut the equipment cost while maintaining the high reliability of its insulation performance, it is necessary 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 preceding paper, lightning surge waveforms and disconnector switching surge waveforms at UHV, 500 kV, and 275 kV substations were analyzed and five to six non-standard lightning surge waveforms with basic frequencies of 0.6 to 5.0 MHz were identified. In this paper, the dielectric breakdown voltage - time characteristics were measured under several different conditions mainly for the quasi-uniform SF6 gas gaps that represent an insulation element of a GIS toward four kinds of non-standard lightning impulse waveforms associated with lightning surges. As a result, in the tested range, the dielectric breakdown values for nonstandard lightning impulse waveforms were higher than for the standard lightning impulse waveform by 3% to 32%.