The long-wavelength stability of an unsupported multilayer liquid film falling under the effects of gravity and surface tension is investigated. By considering the Navier–Stokes equations for two fluid layers in the high-Reynolds-number and small-aspect-ratio limits the steady-state solutions are obtained. The stability criterion found by Lin (J Fluid Mech 104:111–118, 1981) for a one-layer fluid curtain is generalised to the two-layer case and the criterion for an n-layer curtain is established.