Abstract: A combined floor cleaning and floor polishing machine comprises a motor housing (1), an inclined operator handle (2), a base (3) with castors (4) and a motor-operated shaft (5) for a rotating disc (7) supporting interchangeably a cleaning pad or polishing pad, so that the machine weight is carried partly on the pad and partly on the castors (4). If the handle (2) is tilted the machine moves laterally to one side or other in dependence upon the direction of tilt. The use of elastomeric torsion blocks (8) to connect the motor housing (1) to the base (3) provides an elastic resistive force in either tilt direction and thus improves controllability of the cleaning/polishing movement in either lateral direction, by a simple, robust and inexpensive construction.