A method for operating a converter circuit is specified with the converter circuit having a converter unit with a multiplicity of controllable power semiconductor switches and having an energy storage circuit formed by two series-connected capacitors, in which the controllable power semiconductor switches are controlled by means of a control signal formed from a hysteresis signal vector (x), and the hysteresis signal vector (x) is formed from a difference-phase connection current vector (.DELTA.i.sub.fi,i) by means of a hysteresis regulator, and the difference-phase connection current vector (.DELTA.i.sub.fi,i) is formed from the subtraction of a phase connection current vector (i.sub.fi,i) from a reference phase connection current vector (i.sub.fi,i,ref), with the reference phase connection current vector (i.sub.fi,i,ref) being formed from a difference power value (P.sub.diff), a difference wattless-component value (Q.sub.diff) and a phase flux vector (.psi..sub.g,.alpha..beta.). In order to very largely stabilize the switching frequency of the controllable power semiconductor switches, a current correction value (i.sub.0) is additionally subtracted in order to form the difference-phase connection current vector (.DELTA.i.sub.fi,i), with the current correction value (i.sub.0) being formed by integration of a phase connection voltage mean value (u.sub.inv,A), and the phase connection voltage mean value (u.sub.inv,A) being formed by determining the arithmetic mean value of the phase connection voltages (u.sub.inv,iM) with the reference point of the connection point of the capacitors in the energy storage circuit. A device is also specified, by means of which the method can be carried out in a particularly simple manner.