The self-excited global instability mechanisms existing in flat-plate laminar separation bubbles are studied here, in order to shed light on the causes of unsteadiness and threedimensionality of unforced, nominally two-dimensional separated flows. The presence of two known linear global mechanisms, namely an oscillator behaviour driven by local regions of absolute inflectional instability and a centrifugal instability giving rise to a steady three-dimensionalization of the bubble, is studied in a series of model separation bubbles. These results indicate that absolute instability, and consequently a global oscillator behaviour, does not exist for two-dimensional bubbles with a peak reversed-flow velocity below 12 % of the free-stream velocity. However, the threedimensional instability becomes active for recirculation levels as low as u rev ≈ 7 %. These findings suggest a route to the three-dimensionality and unsteadiness observed in experiments and simulations substantially different from that usually found in the literature of laminar separation bubbles, in which two-dimensional vortex shedding is followed by three-dimensionalization.