This study explores coherent structures in a swirling turbulent jet. Stationary axisymmetric solutions of the Reynolds–Averaged Navier–Stokes equations at Re = 200, 000 were obtained using an open source computational fluid dynamics code and the Spalart–Allmaras eddy viscosity model. Then, resolvent analysis with the same eddy viscosity field provided coherent structures of the turbulent fluctuations on the base flow. As in many earlier studies, a large gain separation is identified between the optimal and sub-optimal resolvent modes, permitting a focus on the most amplified response mode and its corresponding optimal forcing. At zero swirl, the results indicate that the jet’s coherent response is dominated by axisymmetric (m = 0) structures, which are driven by the usual Kelvin–Helmholtz shear amplification mechanism. However, as swirl is increased, different coherent structures begin to dominate the response. For example, double and triple spiral (|m|=2 and |m|=3) modes are identified as the dominant structures when the axial and azimuthal velocity maxima of the base flow are comparable. In this case, distinct co- and counter-rotating |m|=2 modes experience vastly different degrees of amplification. The physics of this selection process involve several amplification mechanisms contributing simultaneously in different regions of the mode. This is analysed in more detail by comparing the alignment between the wavevector of the dominant response mode and the principal shear direction of the base flow. Additional discussion also considers the development of structures along the exterior of the jet nozzle.