A process for sealing containers that contain substances for medical, pharmaceutical or cosmetic applications, wherein the containers are conveyed automatically, by means of a conveyor, past at least one processing station or pass it for the treatment or processing, in which process a plurality of containers is conveyed by the conveyor while being held by a carrier (25; 134) in a regular arrangement, and the containers held by the carrier (25; 134) are raised to a raised position for the treatment or processing at or in the respective processing station and are lowered after the treatment or processing, to be held again by the carrier in the regular arrangement, wherein the treatment or processing comprises the filling of the containers with the substance while being held by the carrier, and the step of weighing the containers before the filling and after the filling, wherein the process further comprises the step of sealing the containers, wherein the step of sealing the containers comprises the following steps: pushing caps onto the upper rims of the containers before or after the filling, and pressing supporting surfaces on which the bottoms of the containers are directly supported against each other so that the caps are pushed down onto the containers and these are thereby sterile sealed; wherein the containers are supported in openings or apertures of the carrier in the regular arrangement, wherein at least two resilient holding tabs are respectively associated with the openings or apertures and wherein the containers are respectively supported by the holding tabs in the region of a constricted neck portion below an expanded upper rim at an upper end of the respective container with a radial clearance and with an axial clearance or with a radial clearance and freely displaceable in axial direction before the pushing down of the caps a plurality of containers is conveyed by the conveyor while being held by a carrier (25; 134) in a regular arrangement, and the containers held by the carrier (25; 134) are raised to a raised position for the treatment or processing at or in the respective processing station and are lowered after the treatment or processing, to be held again by the carrier in the regular arrangement, wherein the treatment or processing comprises the filling of the containers with the substance while being held by the carrier, and the step of weighing the containers before the filling and after the filling, wherein the process further comprises the step of sealing the containers, wherein the step of sealing the containers comprises the following steps: pushing caps onto the upper rims of the containers before or after the filling, and pressing supporting surfaces on which the bottoms of the containers are directly supported against each other so that the caps are pushed down onto the containers and these are thereby sterile sealed; wherein the containers are supported in openings or apertures of the carrier in the regular arrangement, wherein at least two resilient holding tabs are respectively associated with the openings or apertures and wherein the containers are respectively supported by the holding tabs in the region of a constricted neck portion below an expanded upper rim at an upper end of the respective container with a radial clearance and with an axial clearance or with a radial clearance and freely displaceable in axial direction before the pushing down of the caps pushing caps onto the upper rims of the containers before or after the filling, and pressing supporting surfaces on which the bottoms of the containers are directly supported against each other so that the caps are pushed down onto the containers and these are thereby sterile sealed; wherein the containers are supported in openings or apertures of the carrier in the regular arrangement, wherein at least two resilient holding tabs are respectively associated with the openings or apertures and wherein the containers are respectively supported by the holding tabs in the region of a constricted neck portion below an expanded upper rim at an upper end of the respective container with a radial clearance and with an axial clearance or with a radial clearance and freely displaceable in axial direction before the pushing down of the caps