A traction drive axle is provided for providing an all-wheel drive operating mode. The traction drive axle includes a unique double enveloping worm/worm gear transmission. A worm is driven by a propshaft which is meshingly engaged with an enveloping worm gear. The enveloping worm gear is selectively coupled via first and second clutches to left and right axle shafts. A control system is provided for controlling actuation of the first and second clutches upon detection of relative rotation between the left and right axle shafts.