An electric drive transmission for a skid steered vehicle has a central casing housing a pair of propulsion motors comprising respective stators and rotors, each rotor being coupled to drive a respective through shaft via a respective epicyclic gear change mechanism. The through shafts are coupled at their inboard ends to a controlled differential with an input from a steer motor, and are coupled at their outboard ends to respective epicyclic gear reduction mechanisms. The through shafts are supported in the casing by respective bearings and the propulsion motor rotors are supported on the through shafts by respective bearings. By supporting the rotors on the through shafts rather than in separate bearings to the casing the diameter and speed rating of the requisite rotor bearings can be reduced.