A method is presented for determining the swirling compressible flow through a nozzle, given conditions at a reference section. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual for the radial velocity component to be neglected at each section, i e, the usual assumption of one-dimensional compressible flow theory. This method is used to determine choked-flow conditions in the case where there is solid-body rotation at the throat for a range of swirl intensities with the ratio of the specific heats taking various values. Mass-flux coefficients and impulse functions are determined. Sonic surfaces, velocity profiles and other characteristics of interest are also presented. An approximate analysis valid for low swirl intensities is developed and analytical formulae are derived for most quantities of interest. The main conclusion of practical importance is that the introduction of swirl to compressible nozzle flows need not lead to a significant reduction in specific thrust. Further exploration of the possible effects of swirl on noise during the relatively short take-off and landing periods cannot therefore be ruled out on the grounds that swirl would lead to excessive thrust losses.