The present invention is related to a cap assembly which is put over a mouth of a bottle and a method for capping of capping the cap assembly to a bottle, and includes a function that makes it possible to open an inner stopper only by operating a cap when removing the cap initially, and makes attaching thereof to the bottle easy. There are included an inner stopper 40 and a cap 50, which respectively include a male screw thread 411c and a female screw thread 541, and the inner stopper 40 and the cap 50 while a state in which they are assembled is maintained are capped to a bottle 60, and when the cap 50 is removed initially, the cap 50 is firstly rotated in a direction of closing to have a junction section 52 broken, and then the cap 50 is rotated in a direction of opening so that the lid body 42 of the inner stopper 40 is removed together with cap 50, thereby causing the inner stopper 40 also to be in a state of being opened.