An apparatus for cleaning domestic and industrial surfaces includes a box-like machine body having a suction system and a steam generation system housed therein, and defining a front portion and an opposite rear portion; a joint for the end of a first suction and steam carrying flexible duct; the machine body having an additional multifunctional suction and steam delivery unit which is overhangingly supported by the machine body between two bilateral support arms hinged to the machine body, and extending beyond the front portion of the machine body.