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Large-eddy simulations (LES) based on scale-selective implicit filtering are carried out in order to study the effect of nozzle pressure ratios on the characteristics of highly underexpanded jets. Pressure ratios ranging from 4.5 to 8.5 with Reynolds numbers of the order 75 000–140 000 are considered. The studied configuration agrees well with the classical picture of the structure of highly underexpanded jets. Similarities and differences between simulation and experiments are discussed by comparing the concentration field structures from LES and planar laser induced fluorescence data. The transient stages, leading eventually to the highly underexpanded state, are visualized and investigated in terms of a phase diagram revealing the shock speeds and duration of the transient stages. For the studied nozzle pressure ratio range, the Mach disk dimensions are found to be in good agreement with literature data and experimental observations. It is observed how the nozzle pressure ratio influences the Mach disk width, and thereby the slip line separation, which leads to co-annular jets with inner and outer shear layers at higher pressure ratios. The improved mixing with increasing pressure ratio is demonstrated by the probability density functions of the concentration. The coherent structures downstream of the Mach disk are identified using proper orthogonal decomposition (POD). The structures indicate a helical mode originating from the shear layers of the jet. Despite the relatively low energy content of the dominant POD modes, the frequencies of the POD time coefficients explain the dominant frequencies in the pressure fluctuation spectra.