An apparatus (1) serves for cleaning surfaces on boards, for instance, and has a cleaning device (2) which is circumferentially continuous and has an upper strand (2) and a lower strand (4) and two guide pulleys (5, 6) in between. The one strand is the cleaning strand which is held by a guide (8) and is pressed onto the surface to be cleaned. A carrier belt (7) is recessed or flattened in some regions of at least one longitudinal side and is therefore narrower in relation to the rest of its longitudinal area. At least one part (8a) at the entrance end of the guide (8) as considered in the feed direction of the cleaning strand, is deflectable or flexible outwardly from the feed direction and can thereby be applied to the inside (7a) of the carrier belt (7). The guide (8) has a substantially C-shaped cross section accommodating the entire width of the carrier belt (7). A narrower slot (10) of the guide (8) has a width smaller than that of the carrier belt (7), but equal to or greater than the recessed or flattened area of the carrier belt (7), so that when the part (8a) is deflected this recessed area of the carrier belt (7) enters the guide (8) and the following wider area of the carrier belt (7) is threaded into the guide.