An electric drive system for a motor vehicle includes a first electric engine having a first rotor, a second electric engine having a second rotor, and a planetary transmission, which has a first planetary gear set, a second planetary gear set, a first input shaft, a second input shaft, a first output shaft and a second output shaft. The first input shaft is designed to introduce first torques originating from the first electric engine into the planetary transmission. The second input shaft is designed to introduce second torques originating from the second electric engine into the planetary transmission. The first output shaft is designed to divert third torques from the planetary transmission. The second output shaft is designed to divert fourth torques from the planetary transmission.