An electric drive system for a motor vehicle includes a first electric machine having a first rotor, a differential having a differential input shaft and a first differential output shaft and a second differential output shaft. The two differential output shafts are arranged coaxially with respect to the first rotor. A first side shaft is coupled to the first differential output shaft for conjoint rotation. A second side shaft is coupled, or is couplable, to the second differential output shaft for conjoint rotation. A second electric machine has a second rotor arranged coaxially with respect to the first rotor. A first switching element is configured to couple the first rotor to the first side shaft for conjoint rotation. A second switching element is configured to couple the second rotor to the second side shaft for conjoint rotation. The first rotor is coupled, or couplable, to the differential input shaft for conjoint rotation.