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Experimental data on the propagation of streamers in mineral oil is important for the design of high-voltage systems in the power and pulsed-power industries. In the present study, breakdown voltages and pre-breakdown delay times were measured for plane-parallel electrodes, and for two non-uniform electrode arrangements. For each geometry, the breakdown characteristics were determined for impulses of rise-time 100 ns, and also rise-time 1 μs. The maximum rate of voltage rise (dV/dt) was 4 MV/μs. For the non-uniform geometries with inter-electrode gap length of 8.5 mm, the time to breakdown was 2.5-3 times longer for impulses of rise-time 1 μs than for 100 ns risetime. The time-to-breakdown data suggest that streamer propagation velocity increases with higher values of dV/dt. For example, the estimated propagation velocity for pinplane geometry with a 1 μs rise-time is 10-12 km/s. At 100 ns rise-time for the same electrode geometry, the average propagation velocity exceeds 40 km/s. The results are compared with data previously generated in parallel liquid-solid gaps, and it is concluded that the time to breakdown is longer, and that higher applied fields are required to initiate breakdown, in open oil gaps compared to the case when a solid spacer is present. The results presented are intended to provide reference data for designers of oil-immersed, high-voltage systems such as power transformers and pulsed-power supplies.