Unsteady circular jets are treated experimentally and numerically. The time evolution of circular pulse jets is investigated systematically for a wide range of jet strength, with the focus on the jet evolution, in particular the formation processes of Mach disks in the middle stage and of shock-cell structures in the later stage. It is shown that unsteady second shocks are realized for all sonic underexpanded jets and they either breed conical shocks for lower pressure ratios or truncated cones (Mach disk and reflected shock) for higher pressure ratios. The vortex ring produced near the nozzle lip plays an important role in the formation of the shock-cell structure. In particular, interactions between the vortex ring and the Mach disk connected with a strong second shock affect remarkably the formation process of the first shock cell. Different formation processes of the first cell structure are found. It is also made clear that the Kelvin–Helmholtz instability along slip surfaces originating from the triple point at the outer edge of the Mach disk is responsible for the generation of large second vortices which entrain the first vortex. This results in strong mixing between the primary jet and surrounding gas for higher pressure ratios. Numerical simulations with a TVD-scheme for the Euler equations are also performed and the numerical results are compared with the experimental ones to understand and predict the flow characteristics of the pulse jets.