The Extrap T1 device is a high aspect ratio toroidal pinch with the dimensions R/a = 0.5 m/0.057 m. In the experiments described here, the stainless steel bellows vacuum vessel was surrounded by a resistive shell with a perpendicular field penetration time of 75-mu-s. The ULQ discharges, with toroidal currents in the range 20-50 kA and pulse lengths up to 2 ms, showed the typical step-wise decay of the plasma current. The current steps corresponded to transitions of the edge q-value across rational values 1/4, 1/3, 1/2, and 1. During a step through a rational q value, there was an increase in the fluctuation activity and a corresponding increase in the plasma resistance. As part of the ULQ studies, discharges with four poloidal field nulls were produced by applying an octupole magnetic field, thus demonstrating that it is possible to sustain ULQ equilibria with poloidal field x-points and a magnetic separatrix. In another study, the transition from ULQ discharges to relaxed state discharges was investigated. When the initial bias toroidal field was reduced so that q was less than about 1/6, which corresponded to a pinch parameter (Kelvin) of about 0.6, a change in the discharge character was observed. The loop voltage required to sustain a given current increased and stochastic fluctuations were seen. Toroidal flux was generated and relaxed state equilibria developed. For higher (Kelvin), in the range of 1.5 to 2.0, a reversed field pinch could be set up if the toroidal field power supply provided a reversed current in the coils. The plasma resistivity was again lower and the pulse lengths in the RFP mode were up to 1 ms, corresponding to over 10 shell penetration times.