The boundary between absolute and convective (linear) instability of two‐dimensional inertial jets and wakes is determined as a function of the ratio of jet/wake to ambient density, as well as the ratio of mixing layer thickness to jet/wake width, the velocity ratio, and the Reynolds number. For this, a viscous, heat‐conducting ideal gas is taken as the fluid, a zero Mach number, no buoyancy and a parallel basic flow are assumed, and the density variation is achieved by specifying a mean temperature profile similar to the velocity profile. Considering both ‘‘varicose’’ and ‘‘sinuous’’ disturbances, results are obtained for the inviscid top‐hat jet/wake bounded by two vortex sheets, the inviscid jet with continuous velocity and density profiles, and the viscous wake. For the latter, both constant and temperature‐dependent viscosity are investigated. In all the cases it is found that low density of thehigh‐speed fluid promotes absolute instability, while low density of thelow‐speed fluid has the opposite effect. By comparison with experiments it is shown that the present results provide useful information about the parameter range in which flow oscillations are self‐excited.