A steering gear mechanism for motor vehicles may include a steering system housing in which a toothed rack is mounted and displaceable along a longitudinal axis. The toothed rack may be connected to steerable wheels of a motor vehicle and configured to pivot the steerable wheels. The toothed rack can include a first toothed segment that meshes with a first pinion of a pinion shaft, with the pinion shaft being connected to a steering wheel via a steering shaft. The toothed rack may further include a second toothed segment that is situated opposite the first toothed segment with respect to the longitudinal axis and engages with a second pinion. Further, an electric motor can drive the first pinion in a first direction, which by way of direct or indirect coupling causes the second pinion to rotate in a second direction opposite the first direction. The electric motor may in some cases be in the form of a hollow-shaft motor that at least partially surrounds the input shaft and/or the pinion shaft.