The invention relates to a connection system having a first connection part which defines a first passage and to a second connection part to be connected to the first connection part which defines a second passage which is orientated with the first passage in the connected state of the connection parts, wherein the first connection part has a blunt cone section through which the first passage extends and the second connection part has a reception section having a frustoconical reception space for receiving the blunt cone section into which the second passage opens.