Container system having at least two containers (B1, B2, B3) and a connecting system for providing a fluidic connection between the containers (B1, B2, B3), wherein the connecting system comprises at least two connecting arrangements (3A', 3B') configured to produce the fluidic connection, namely a first connecting arrangement and a second connecting arrangement, which are each fluidically sealed in an initial state and can be opened in an opening region (4A', 4B') to produce the fluidic connection, wherein the containers (B1, B2, B3) each comprise one of the connecting arrangements (3A', 3B'), wherein at least one of the containers (B1, B2, B3) comprises a sealing arrangement which uninterruptedly seals off a volume which is in direct contact with the opening region (4A', 4B') during a movement of the connecting arrangements (3A', 3B') relative to one another, wherein the connecting arrangements (3A', 3B') are configured for mutual opening by breaking through frangible points of the opening regions (4A', 4B'), whereby the continuous fluidic connection is producible by irreversible destruction of the opening regions (4A', 4B'), and wherein the connecting arrangements (3A', 3B') comprise mouth-like portions (5A', 5B'), wherein the mouth-like portion of the first connecting arrangement is adapted to be inserted into the mouth-like portion of the second connecting arrangement such that during the insertion the opening region of the second connecting arrangement is opened, wherein the connecting arrangements (3A', 3B') have different connecting positions with one another, wherein the connecting arrangements (3A', 3B') are configured to open none or only one of the first and second connecting arrangements (3A', 3B') on reaching a first connecting position and to provide the continuous fluidic connection and/or the opening of the two connecting arrangements (3A', 3B') on reaching another, second connecting position, wherein the sealing arrangement seals or closes off the volume without interruption in the first connecting position, in the second connecting position and between the first and second connecting positions, characterized in that the connecting arrangements (3A', 3B') are connected to one another non-releasably in the first connecting position. wherein the containers (B1, B2, B3) each comprise one of the connecting arrangements (3A', 3B'), wherein at least one of the containers (B1, B2, B3) comprises a sealing arrangement which uninterruptedly seals off a volume which is in direct contact with the opening region (4A', 4B') during a movement of the connecting arrangements (3A', 3B') relative to one another, wherein the connecting arrangements (3A', 3B') are configured for mutual opening by breaking through frangible points of the opening regions (4A', 4B'), whereby the continuous fluidic connection is producible by irreversible destruction of the opening regions (4A', 4B'), and wherein the connecting arrangements (3A', 3B') comprise mouth-like portions (5A', 5B'), wherein the mouth-like portion of the first connecting arrangement is adapted to be inserted into the mouth-like portion of the second connecting arrangement such that during the insertion the opening region of the second connecting arrangement is opened, wherein the connecting arrangements (3A', 3B') have different connecting positions with one another, wherein the connecting arrangements (3A', 3B') are configured to open none or only one of the first and second connecting arrangements (3A', 3B') on reaching a first connecting position and to provide the continuous fluidic connection and/or the opening of the two connecting arrangements (3A', 3B') on reaching another, second connecting position, wherein the sealing arrangement seals or closes off the volume without interruption in the first connecting position, in the second connecting position and between the first and second connecting positions, characterized in that the connecting arrangements (3A', 3B') are connected to one another non-releasably in the first connecting position.