A tensioning device is so constructed that even thin-wall parts to be clamped can be secured and clamped reliably radially as to a driving shaft. During tensioning procedure, radial forces need not be taken up by a part to be clamped. For this purpose a force taking-up part is provided which is seated in a region of tensioning cones upon this part to be clamped or secured. For this reason very thin-wall construction can be employed and nevertheless reliable clamping radially upon the driving shaft can occur because the force taking-up part hinders and prevents that any thin-wall part is radially widened and expanded. With the tensioning device therefore it is also possible to clamp thin-wall parts, as for example thin-wall hollow shafts, with coarse-tolerance driving shafts and with driving shafts of differing basic diameter to be clamped radially in a reliable manner. Upon one of the parts to be clamped in a region of tensioning cones at least one force taking-up part is arranged which receives and takes up the radial forces encountered during tensioning procedure and being operatively connected with a tensioning element.