Rechargeable battery assembly (100; 200; 300; 400; 500; 600), comprising: a first rechargeable battery unit having a first terminal and a second terminal; a second rechargeable battery unit having a first terminal and a second terminal, said second rechargeable battery unit being connected in series with the first rechargeable battery unit; and a differential amplifier having an inverting input, a non-inverting input and an output, at which an amplified difference between the signal at the inverting input and the signal at the non-inverting input is present; wherein - the non-inverting input of the differential amplifier is connected to the second terminal of the first rechargeable battery unit and to the first terminal of the second rechargeable battery unit, - the inverting input of the differential amplifier is coupled to the first terminal of the first rechargeable battery unit and to the second terminal of the second rechargeable battery unit, and - the output of the differential amplifier is connected to the second terminal of the second rechargeable battery unit; characterized in that a coupling element having two load terminals is connected between the output of the differential amplifier and the second terminal of the second rechargeable battery unit, which coupling element enables the second rechargeable battery unit to be charged via the coupling element, but permits at most slight discharging of the second rechargeable battery unit in the direction of the output of the differential amplifier, wherein the first pole of the first rechargeable battery unit and the second pole of a third series-connected rechargeable battery unit serve as a voltage supply or a reference for the differential amplifier. a first rechargeable battery unit having a first terminal and a second terminal; a second rechargeable battery unit having a first terminal and a second terminal, said second rechargeable battery unit being connected in series with the first rechargeable battery unit; and a differential amplifier having an inverting input, a non-inverting input and an output, at which an amplified difference between the signal at the inverting input and the signal at the non-inverting input is present; wherein - the non-inverting input of the differential amplifier is connected to the second terminal of the first rechargeable battery unit and to the first terminal of the second rechargeable battery unit, - the inverting input of the differential amplifier is coupled to the first terminal of the first rechargeable battery unit and to the second terminal of the second rechargeable battery unit, and - the output of the differential amplifier is connected to the second terminal of the second rechargeable battery unit; - the non-inverting input of the differential amplifier is connected to the second terminal of the first rechargeable battery unit and to the first terminal of the second rechargeable battery unit, - the inverting input of the differential amplifier is coupled to the first terminal of the first rechargeable battery unit and to the second terminal of the second rechargeable battery unit, and - the output of the differential amplifier is connected to the second terminal of the second rechargeable battery unit; characterized in that a coupling element having two load terminals is connected between the output of the differential amplifier and the second terminal of the second rechargeable battery unit, which coupling element enables the second rechargeable battery unit to be charged via the coupling element, but permits at most slight discharging of the second rechargeable battery unit in the direction of the output of the differential amplifier, wherein the first pole of the first rechargeable battery unit and the second pole of a third series-connected rechargeable battery unit serve as a voltage supply or a reference for the differential amplifier.