Abstract
On a solid substrate, superfluid 4He may show stratified liquid films (above a solid 4He layer). Assuming the existence of these films, we analyse the dynamics of wetting for a two-layer droplet which tends to spread and transform into a one-layer droplet (at low temperature: no vapour phase is present). The permeation process between layers, which exists in classical liquids, is replaced here by a Josephson coupling. Spreading should occur via Josephson vortices that drift towards the centre of the droplet.