A method for processing containers includes, for each container to be processed: a) an assembling step of assembling a cap having a cover on a container, the cap including a tubular base and a cover pivotably connected to the base, between an open position and a closed position, the cap being assembled via the base thereof onto the container at an opening of the container, b) a step of sterilizing the container provided with the cap having a cover, and c) a step of filling the container, the filling step including filling the container with a filling product while the cap having the cover is in the open position, and moving the cover into the closed position.