An improved volume-averaged global model is developed for a cylindrical electronegative (EN) plasma that is applicable over a wide range of electron densities, electronegativities, and pressures. It is applied to steady and pulsed-power oxygen discharges. The model incorporates effective volume and surface loss factors for positive ions, negative ions, and electrons combining three EN discharge regimes: a two-region regime with a parabolic EN core surrounded by an electropositive edge, a one-region parabolic EN plasma, and a one-region flat-topped EN plasma, spanning the plasma parameters and gas pressures of interest for low pressure. Pressure-dependent effective volume and surface loss factors for the neutral species, and an updated set of reaction rate coefficients for oxygen based on the latest results were incorporated. The model solutions yield important processing quantities as the neutral/ion flux ratio, with the discharge aspect ratio, pulsed-power period, and duty ratio as parameters. For steady discharges, increasing 2R/L from 1 to 6 leads to a factor of 0.45 reduction in the neutral/ion flux ratio. For pulsed discharges with a fixed duty ratio, this ratio is found to have a minimum with respect to pulse period, and a 25% duty ratio pulse reduces it by a factor of 0.75 compared to the steady-state case. A configuration of both theoretical and practical interest is a capacitive discharge connected through a dielectric or metal slot to a peripheral grounded region. The configuration is used in commercial dual frequency capacitive discharges, where a dielectric slot surrounding the substrate separates the main plasma from the peripheral grounded pumping region. Ignition of the peripheral plasma produces effects such as poor matching and relaxation oscillations that are detrimental to processing performance. Discharge models are developed for diffusion and plasma maintenance in the slot, and plasma maintenance in the periphery. The theoretical predictions of ignition conditions as a function of voltage and pressure are compared with experimental results for a driving frequency of 27.12 MHz and a gap spacing of 0.635 cm connecting the two regions, giving good agreement. Instabilities associated with the loss of confinement in both the kilohertz and hertz frequency range are discovered, and a physical model for the kilohertz frequency range instability is proposed.