Abstract: A saw-blade tensioning arrangement for band saw and like machines which includes a hydraulic cylinder (6) having arranged for movement therein a piston (7) which is intended to activated saw-blade tension control means (2). The blade tension is, in this way, dependent on the hydraulic pressure in the cylinder. The arrangement includes means for pneumatically regulating the hydraulic pressure, these means including a pneumatically operated pressure booster (10) and means (19, 20, 35) for activating the pressure booster at the end of a working stroke of the hydraulic piston, therewith to tension the saw blade to the desired working tension, this working tension being determined, inter alia, by the blade width.