The flow in a centrifugal compressor has been computed using large eddy simulation (LES). The investigated geometry is that of a ported shroud compressor with a 10 blade impeller with an exducer diameter of 88 mm. The computational data compares favorably with measured data for the same compressor and operational point. For the considered operational point near surge, the flow field in the entire compressor stage is unsteady. Back-flow occurs in the diffuser, wheel, and the ported shroud channels resulting in back-flow at the walls in the inlet region of the compressor. In the diffuser and volute, the flow is highly unsteady with perturbations that are convected around the volute, affecting the flow field in most of the entire compressor. The mechanism driving this unsteadiness is assessed by flow visualizations, frequency analysis, and correlations of pressure and velocity data in order to gain a more comprehensive understanding of the mechanism leading to stall and surge.