The invention concerns a plastic closure part (10) which can be fixed to a container or a further closure part to be fixed to the container, comprising a tubular discharge portion (3) whose cross-section is closed by a membrane (7) which has a tear line (8) extending peripherally over more than 180° along its outer edge and a corresponding method for the production of such a closure. In order to develop a closure part having the features set forth in the opening part of this specification and a method for the production thereof to the effect that the problems occurring upon injection moulding due to narrow flow passages are eliminated it is provided according to the invention that the tear line (8) is formed by a cut introduced into the material of the membrane (7) with a cutting or punching tool.