A clamp structure with a clamping band having open ends and a mechanical interconnection of the open ends of the band that include at least two outwardly extending hooks in the inner band portion adapted to engage in apertures in the outer band portion; at least one of the hooks is a cold-deformed support hook and another one of the hooks is a generally circumferentially extending combined guide and support hook which has an inclined guide and support surface operable to initially engage with the corresponding aperture in the outer band portion so as to guide the inner and outer band portions toward one another while at the same time absorbing circumferentially directed tightening forces until the cold-deformed support hook becomes effective in also absorbing tightening forces by engagement of its abutment surface with the corresponding aperture.