A closure capsule for closing a container, comprising: - a cap that can be associated with a container and comprising a frangible mouth; - a cutter comprising a cutting edge designed to open said frangible mouth; at least said cap and said cutter in combination defining a reservoir for containing a substance to be dropped into the container when the frangible mouth is opened; - a covering that protects the cap and the cutter; said covering being separate from the cutter and, in turn, comprising: i) a lateral wall that encloses a zone for at least partially housing the cutter; ii) a base from which said lateral wall extends; - means for transmitting an opening torque, from the covering to the cutter, for opening the frangible mouth, said transmitting means comprising a first and a second portion (51, 52) incorporated in the covering and in the cutter, respectively; said first portion being incorporated in the base; characterized in that the transmitting means, when enmeshed, enables a solidly rotational-translational movement of the covering and of the cutter; the transmitting means, when enmeshed, thus enables the transmission of the opening torque of the frangible mouth without relative sliding between the covering and the cutter. - a cap that can be associated with a container and comprising a frangible mouth; - a cutter comprising a cutting edge designed to open said frangible mouth; at least said cap and said cutter in combination defining a reservoir for containing a substance to be dropped into the container when the frangible mouth is opened; - a covering that protects the cap and the cutter; said covering being separate from the cutter and, in turn, comprising: i) a lateral wall that encloses a zone for at least partially housing the cutter; ii) a base from which said lateral wall extends; - means for transmitting an opening torque, from the covering to the cutter, for opening the frangible mouth, said transmitting means comprising a first and a second portion (51, 52) incorporated in the covering and in the cutter, respectively; said first portion being incorporated in the base; characterized in that the transmitting means, when enmeshed, enables a solidly rotational-translational movement of the covering and of the cutter; the transmitting means, when enmeshed, thus enables the transmission of the opening torque of the frangible mouth without relative sliding between the covering and the cutter. i) a lateral wall that encloses a zone for at least partially housing the cutter; ii) a base from which said lateral wall extends; - means for transmitting an opening torque, from the covering to the cutter, for opening the frangible mouth, said transmitting means comprising a first and a second portion (51, 52) incorporated in the covering and in the cutter, respectively; said first portion being incorporated in the base; characterized in that the transmitting means, when enmeshed, enables a solidly rotational-translational movement of the covering and of the cutter; the transmitting means, when enmeshed, thus enables the transmission of the opening torque of the frangible mouth without relative sliding between the covering and the cutter. - means for transmitting an opening torque, from the covering to the cutter, for opening the frangible mouth, said transmitting means comprising a first and a second portion (51, 52) incorporated in the covering and in the cutter, respectively; said first portion being incorporated in the base;