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A continuum model of direct current (dc) and 13.56-MHz radio-frequency (RF) discharges in a parallel-plate configuration is presented. The model consists of equations for electron and ion continuity, Poisson's equation for the self-consistent electric field, and an equation for electron energy. The equations are solved for a single set of conditions and a comparison is made between the structure of a dc and a 13.56-MHz RF discharge. One of the major structural differences is the emergence, under RF conditions, of large electron conduction currents in the quasi-neutral region. This results in substantially higher electron heating in the quasi-neutral region and a consequent shift in the peak ionization rate from the cathode sheath to the quasineutral region. In addition, the RF solutions suggest that equivalent circuit models and ambipolar diffusion models are promising ways to simplify predictions of discharge physics. The ultimate goal of this work is to provide an adequate description of the discharge physics so that discharge chemistry can be understood. The latter is essential in predicting the behavior of plasma film etching and deposition reactors used extensively in electronics materials processing.