In this work, we study the shape and dynamics of helical coherent structures found in the flow field of an annular swirling jet undergoing vortex breakdown. The flow field is studied by means of time-resolved Tomographic Particle Image Velocity (Tomo-PIV) measurements. The obtained flow fields are analyzed using classical and spectral proper orthogonal decomposition. Despite the simple geometrical setup of an annular jet, the flow field of is very complex. Two distinct helical flow structures are identified: a single and double helix and these structures are not higher harmonics of each other. The structures have a relatively low energy content which makes it hard to separate them from other motions in the flow field. As such, POD fails to identify them. Spectral POD on the other hand can identify them accurately if the filter size is around 8 times the precession period, which proves that SPOD is a powerful tool to analyze these kind of flows.