The present invention refers to a floor washing-drying machine, in particular of the drives-on-board kind, provided with at least a front driving and steering wheel (3), a pair of rear wheels (5), a brush-carrying head (4) positioned between the front driving wheel and the supporting axle of the rear wheels, and a wiping and vacuuming device (6) arranged behind the rear wheels. The brush-carrying head (4) is connected with the machine frame through a support and steering system of four-arm linkage type (X,Y,J,W; 17,19) which is driven by a gear steering device (11,12,14,15). The technical solution allows to solve efficiently the problem of collecting washing liquid and to dampen impacts of the machine against obstacles which it may encounter along its path.