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The phenomenon of stable persistent currents is central to the studies ofsuperfluidity in a range of physical systems. While all of the previoustheoretical studies of superfluid flows in annular geometries concentrated onconservative systems, here we extend the stability analysis of persistentcurrents to open-dissipative exciton-polariton superfluids. By considering anexciton-polariton condensate in an optically-induced annular trap, we determinestability conditions for an initially imposed flow with a non-zero orbitalangular momentum. We show, theoretically and numerically, that the system cansustain metastable persistent currents in a large parameter region, anddescribe scenarios of the supercurrent decay due to the dynamical instability.

Stability of persistent currents in open-dissipative quantum fluids