A claim (11) in which clamping band portions (11a, 11b, 111a, 111b) intended to form overlapping inner and outer band portions (11a, 11b, 111a, 111b) installed condition that are connected by a connection (31, 32, 131, 170), and which a tightening device (13, 113) for tightening the clamping band (11) about an object to be fastened and an arrangement assuring gap-free and stepless internal clamping surfaces of the clamping band (11) including a male member (61, 161) near the end of the inner band portion (11b, 111b) are provided whereby the male member (61, 161) is adapted to cooperate with a female member (67, 167) in the outer band portion (11a, 111a); a guide arrangement (21, 63’) is further formed by a bent-up tab-like member (21, 121) on each side of the male member (67, 167) and adapted to engage in two guide slots (63’, 163’) of the outer band portion (11a, 111a) to guide relative movement of the inner and outer band portions (11a, 11b, 111a, 111b) during tightening of the tightening device (13, 131); the connection (31, 32, 131, 170) may also include a lost-motion arrangement permitting initial plastic deformation of the tightening device (31, 131) substantially without change in radial dimension.