Submodule for a modular multilevel converter having - an energy store (C 0), - a semiconductor series circuit, which is connected in parallel with the energy store (C 0) and is composed of two power semiconductor switches (T 1, T 2), which can be switched on and off and with each of which a freewheeling diode (D 1, D 2) is connected in parallel in the opposite direction, - a first connection terminal, which is connected to the potential point between the power semiconductor switches (T 1, T 2), - a second connection terminal, and - a snubber network, which has a current rise limiting inductor (L 1) and a demagnetization branch, which bypasses said current rise limiting inductor and in which two snubber diodes (D S1, D S2) arranged in series in the same direction and a snubber resistor (R S) are arranged in series, - wherein the semiconductor series circuit is connected to the energy store (C 0) via the current rise limiting inductor (L 1), - wherein the potential point between the snubber diodes (D S1, D S2) is connected to the potential point between the power semiconductor switches (T 1, T 2) via a snubber capacitor (C S), and - wherein the snubber network does not have any other snubber components, or any other snubber component of the snubber network is arranged in a mesh that is partially formed by the demagnetization branch or sections thereof, - the demagnetization branch is connected both to the potential point between the respectively associated current rise limiting inductor (L1, L2) and the semiconductor series circuit (2, 4) and, with low inductance, to a pole of the respective energy store, and - the second connection terminal is connected to the potential point between the current rise limiting inductor and the semiconductor series circuit, to the potential point between the current rise limiting inductor (L 1) and the energy store (C 0) or to a centre tap of the current rise limiting inductor (L 1), characterized in that - the demagnetization branch has a branch capacitor (C X1, C X2), wherein the branch capacitor (C X1, C X2) is connected in parallel with the snubber resistor (R S1, R S2). - an energy store (C 0), - a semiconductor series circuit, which is connected in parallel with the energy store (C 0) and is composed of two power semiconductor switches (T 1, T 2), which can be switched on and off and with each of which a freewheeling diode (D 1, D 2) is connected in parallel in the opposite direction, - a first connection terminal, which is connected to the potential point between the power semiconductor switches (T 1, T 2), - a second connection terminal, and - a snubber network, which has a current rise limiting inductor (L 1) and a demagnetization branch, which bypasses said current rise limiting inductor and in which two snubber diodes (D S1, D S2) arranged in series in the same direction and a snubber resistor (R S) are arranged in series, - wherein the semiconductor series circuit is connected to the energy store (C 0) via the current rise limiting inductor (L 1), - wherein the potential point between the snubber diodes (D S1, D S2) is connected to the potential point between the power semiconductor switches (T 1, T 2) via a snubber capacitor (C S), and - wherein the snubber network does not have any other snubber components, or any other snubber component of the snubber network is arranged in a mesh that is partially formed by the demagnetization branch or sections thereof, - the demagnetization branch is connected both to the potential point between the respectively associated current rise limiting inductor (L1, L2) and the semiconductor series circuit (2, 4) and, with low inductance, to a pole of the respective energy store, and - the second connection terminal is connected to the potential point between the current rise limiting inductor and the semiconductor series circuit, to the potential point between the current rise limiting inductor (L 1) and the energy store (C 0) or to a centre tap of the current rise limiting inductor (L 1), characterized in that - the demagnetization branch has a branch capacitor (C X1, C X2), wherein the branch capacitor (C X1, C X2) is connected in parallel with the snubber resistor (R S1, R S2).