We show the vapour-driven Marangoni effect as a new paradigm for the continuous self-propulsion of floating soft machines by transduction of chemical energy to motility, featuring a prolonged locomotion at steady velocity with a small amount of on-board fuel. The propulsion is induced by modification of the liquid surface using organic vapour transported through a nanocellulose aerogel membrane. The steady velocity is achieved through a continuous supply of fuel vapour that lowers the surface tension of the liquid, combined with the spontaneous recovery of the surface tension after the floating machine has passed. The membranes are gas permeable from their open-porous nanofibrillar structure and float on water and oils due to their superhydrophobic and superoleophobic nature. The velocity is tunable by selecting solvents with different vapour pressure.