Safety closure has a cap with a security ring for tearing along a peripheral tear line formed on a part of the neck of the container, the peripheral tear line being torn when the container is opened for the first time. A preformed closure cap body of thermoplastic resin is used, the security ring (4) having an annular zone (4a) with a thickened wall between the tear line (5) and its edge zone, the forming of the edge zone (4b) with thinner wall of the security ring on the neck (2) of the container taking place under the action of heat and pressure so that the supplying of heat for plasticising the part with the thickened wall is terminated. The preformed closure cap body pref. has the two zones with different wall thicknesses placed stepwise relative to each other.
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