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An investigation of the near-field flow structure of coaxial jets with large outer to inner velocity ratio r u has been conducted. Since in all cases r u >1, the outer jet dominates the near-field flow structure. Two flow regimes are identified depending on whether r u is larger or smaller than a critical value r uc . When r u < r uc , the fast annular jet periodically pinches the central, slow jet near the end of the inner potential cone. The pinching frequency corresponds to the outer-jet mode. The length of the inner potential cone is strongly dependent on r u and behaves like A / r u , where A depends weakly on the initial conditions. When r u > r uc , the inner potential cone is truncated and is followed by an unsteady recirculation bubble with low-frequency oscillation. The transition from one regime to another is explained by a simple model whose ingredients are the turbulent entrainment rate, governed by the outer-jet mixing layers and mass conservation. This model satisfactorily predicts the dependence of the inner potential cone length on r u and the critical velocity ratio r uc . The recirculation bubble has a wake-type instability. It oscillates at a low frequency and a large amplitude compared to the Kelvin–Helmholtz mode. Angular cross-correlations in the plane parallel to the jet outlet show moreover that this oscillation displays an azimuthal precession such that the rotation time of the phase of the oscillation equals the oscillation period. These salient features are discussed in the framework of the nonlinear delayed saturation (NLDS) model.