In order to guide a cutting band in a band saw machine in a more efficient manner one or two pivotal band guides (1) according to the invention are fitted as close as possible to the cutting place. Each guide (1) is in two parts and designed as a wheel which can run on bearings (5). The wheel consists of two guide rings (2, 3) with side faces (10) forming lateral guides for the side faces of the saw blade (17) or the knife blade (11). At the rear the cutting blade is provided with a bottom guide in the form of a face (13, 19). This may be configured as the periphery of the rings (12, 18, 21). Finally, one or a number of tolerance rings (14, 20) are inserted, permitting adjustment of the distance between the sides faces (10) on a continuous basis. Hereby is obtained a rotary guide (1) which is not exposed to irregular wear since the entire guide is easily brought to rotate when the cutting blade is moved. This gives a hitherto unobtainable good guiding since the cutting band is being guided in all directions of tension during cutting, whereby deformation of the band is avoided. This gives a very accurate guiding without noise and with reduced wear of the cutting band.