The invention relates to a steering system for an agricultural or industrial utility vehicle, especially for a tractor. An electric drive (22, 24) is provided for each half of an axle, preferably a front axle (20), of the utility vehicle (10). Said electric drive can be driven by at least one wheel (26) associated with the each axle half. The electric drive (22, 24) can be controlled in such a manner that predetermined torque can be transmitted from the electric drive (22, 24) to the wheel (26) which is being driven. Preferably, the wheels (14) associated with a mechanical drive axle, particularly a rear axle (12) of the utility vehicle (10), can be driven by a mechanical drive (16, 18) of the utility vehicle (10). The invention also relates to a method for operating a steering system. The aim of the invention is to enable traction forces to be transmitted by wheels (26) driven by the electric drives (22, 24), even when the utility vehicle (10) negotiates bends, whereby particular braking torque should be prevented on said wheels (26) in specific steering angles. The torque which is to be transmitted to the wheel on the outside of the bend is greater that the torque which is to be transmitted to the wheel on the inside of the wheel in order to support or effect the steering of the utility vehicle.