The spectral proper orthogonal decomposition method, which extracts spatially and temporally coherent modes in stationary flowfields, is used in the current paper to analyze high-speed broadband chemiluminescence and shadowgraph videos taken the internal and external flowfields, respectively, of multiple pulsejet engine geometries. By comparing the modes of highest energies across geometric variations of tailpipe length as well as the presence or absence of a nozzle flare at the exit, we showcase features of notable, but hidden, combustion and fluid dynamic interest that help sustain the cyclic and unsteady operation. Two different vortical systems develop internally. The primary is a strong toroidal vortex caused by rapid reed valves’ closure at the headwall. The second is a shedding vortex, which is seen to tear itself apart from the primary vortex due to the inertia of the incoming fresh reactants. Based on the engine geometry, one of the two is shown to be a considerably stronger dynamic flow feature. In the exhaust, the presence of a diverging nozzle flare causes two distinct starting vortices. When the exhaust is just a straight tube, only one starting vortex is formed. We link this to the fluidic piston effect accompanying the Helmholtz resonance in these devices. Point-source pressure sensors are used to complement the information attained from the video analyses.