One wristwatch case, characterized in that a pipe is fixedly connected thereto and a connection interface between the wristwatch case and the pipe is not present substantially; the method of fixing the wristwatch, comprising the steps of providing a through-hole in the wristwatch case, press-fitting the pipe of 0 mm. or larger in press-fitting tolerance (pipe outer diameter - through-hole diameter) between the through-hole and the pipe, and heating the wristwatch case after the press-fitting step; the other wrist-watch case, characterized in that a pipe is fixedly connected thereto through a diffusion layer; the method of fixing the pipe of the wristwatch case, comprising the steps of forming a through-hole in the wristwatch case, press-fitting the pipe of 0 mm. or larger in press-fitting tolerance (outer diameter of pipe having a metal film formed on the surface thereof - diameter of through-hole) between the through-hole and the pipe having a metal film formed on the surface thereof, and heating the wristwatch case in vacuum or reducing gas atmosphere after the press-fitting step.