The present invention refers to a laundry treating machine, such as a dryer or a washer/dryer machine, suitable for applying a steam treatment to laundry. A laundry treating machine according to the invention comprises: a drum (1) having an inner region (3) for receiving laundry to be treated; air conveying means (7, 11) for conveying treating air from and to said drum inner region (3); a condenser (9) for removing moisture from laundry treating air; collecting means (12, 14, 16, 17, 19, 20) for receiving condensate produced by the condenser (9); a steam generator (22) in fluid connection with the collecting means (12, 14, 16, 17, 19, 20) and with the drum inner region (3) for directing steam in said region (3); said machine being characterised in that said collecting means (12, 14, 16, 17, 19, 20) comprise a multiple-way conduit (17, 19, 20) directing said condensate towards a plurality of tanks (14, 16), said conduit (17, 19, 20) being provided with valving means (18) for controlling condensate flow towards said tanks (14, 16).