A clamping device (100; 200) in the type of an outer clamping means for fixing of work pieces, in particular for the purpose of rotating processing, having - a housing (102; 202) extended in an axial direction, - an actuation member (140; 240) movable in axial direction in relation to the housing (102; 202) for the purpose of clamping and de-clamping, - a clamping sleeve (130; 230), and - a multitude of clamping segments (112; 212) and which are arranged inside the clamping sleeve (130; 230) serving for applying force to the work piece, wherein - the clamping sleeve (130; 230) comprises for each clamping segment (112; 212) at its inner side a guide surface (134; 234) inclined in relation to the axial direction, - the clamping segments (112; 212) in each case comprise on their outer side a slide surface inclined in relation to the axial direction, - the clamping sleeve (130; 230) and the entirety of the clamping segments (112; 212) can be relatively displaced to one another in axial direction, in order to hereby achieve a radial displacement of the clamping segments (112; 212) in the case of axial relative displacement, and - the clamping sleeve is axially attached fixed in location to the housing and the clamping segments are axially attached fixed in location to the actuation member or the clamping sleeve is axially attached fixed in location to the actuation member and the clamping segments are axially attached fixed in location to the housing or the clamping sleeve and the clamping segments are coupled to the actuation member such that they can be displaced axially in opposing directions in relation to the housing by means of the actuation member, characterized in that for axial fixed in location coupling of the clamping segments (112; 212) to the housing or to the actuation member at least one coupling element (142; 242) is provided, which is provided axially fixed in location to the housing or to the actuation member and which is engaged axially in a form-fit manner with at least one clamping segment (112; 212) in a coupling region (136; 236) between a guide surface region (134b, 234b) of the guide surface (134; 234) distal in axial direction and a guide surface region (134a; 234a) of the guide surface (134; 234) proximal in axial direction. - a housing (102; 202) extended in an axial direction, - an actuation member (140; 240) movable in axial direction in relation to the housing (102; 202) for the purpose of clamping and de-clamping, - a clamping sleeve (130; 230), and - a multitude of clamping segments (112; 212) and which are arranged inside the clamping sleeve (130; 230) serving for applying force to the work piece, - the clamping sleeve (130; 230) comprises for each clamping segment (112; 212) at its inner side a guide surface (134; 234) inclined in relation to the axial direction, - the clamping segments (112; 212) in each case comprise on their outer side a slide surface inclined in relation to the axial direction, - the clamping sleeve (130; 230) and the entirety of the clamping segments (112; 212) can be relatively displaced to one another in axial direction, in order to hereby achieve a radial displacement of the clamping segments (112; 212) in the case of axial relative displacement, and - the clamping sleeve is axially attached fixed in location to the housing and the clamping segments are axially attached fixed in location to the actuation member or the clamping sleeve is axially attached fixed in location to the actuation member and the clamping segments are axially attached fixed in location to the housing or the clamping sleeve and the clamping segments are coupled to the actuation member such that they can be displaced axially in opposing directions in relation to the housing by means of the actuation member,