Since the experiments of Monkewitz et al. (J. Fluid Mech. vol. 213, 1990, p. 611), sufficiently hot circular jets have been known to give rise to self-sustained synchronized oscillations induced by a locally absolutely unstable region. In the present investigation, numerical simulations are carried out in order to determine if such synchronized states correspond to a nonlinear global mode of the underlying base flow, as predicted in the framework of Ginzburg–Landau model equations. Two configurations of slowly developing base flows are considered. In the presence of a pocket of absolute instability embedded within a convectively unstable jet, global oscillations are shown to be generated by a steep nonlinear front located at the upstream station of marginal absolute instability. The global frequency is given, within 10% accuracy, by the absolute frequency at the front location and, as expected on theoretical grounds, the front displays the same slope as a $k^-$-wave. For jet flows displaying absolutely unstable inlet conditions, global instability is observed to arise if the streamwise extent of the absolutely unstable region is sufficiently large: while local absolute instability sets in for ambient-to-jet temperature ratios $S \le 0.453$, global modes only appear for $S \le 0.3125$. In agreement with theoretical predictions, the selected frequency near the onset of global instability coincides with the absolute frequency at the inlet. For lower $S$, it gradually departs from this value.