The dynamics of countercurrent mixing is examined in the shear layer of an axisymmetric jet. Experiments were designed to establish conditions of absolute instability in a spatially developing shear layer and to document how the instability influences the jet development. By applying suction around the jet periphery, shear-layer velocity ratios R greater than 1 could be studied. Here, R=(U1−U2)/(U1+U2), where U1 is the velocity of the forward jet stream and U2 is the velocity of the counterflowing stream created by suction. The density ratio S=ρ1/ρ2 of the mixing layer was also varied to determine the stability boundary in the S-R plane. The density of the forward stream ρ1 was increased by adding sulfur hexafluoride to the air jet, which provided density ratios between 1 and 5.1. Hot-wire anemometry and flow visualization revealed that a global transition occurs when conditions of absolute instability are established in the jet shear layers. One consequence of this transition is an abrupt decrease in the jet spread rate. The experimentally determined transition between globally stable and globally unstable flow regimes in the S-R plane agrees quite well with predictions of the convective/absolute instability boundary based on the linear stability theory [Pavithran and Redekopp, Phys. Fluids A 1, 1736 (1989)].