Power attachment made to the lower portion of a rail car wheel, at the outer side thereof, to render a railway car selfpropellable bidirectionally. The structure includes a rollercarrying C-clamp which, from a side entry position relative to the car to be moved, draws in with a power clamping action against the tread of the wheel at that side so as to interpose first rollers between the jaws of the clamp and the wheel, and other rollers between the clamp and the rail beneath the car wheel. The structure also includes a power unit for bidirectionally driving the first rollers, for collapsing the Cclamp under power to partially support the wheel on the rail, and for bidirectionally driving a set of extendible ground transport wheels which are provided for the structure and which, when extended from a retracted position, render the attachment selfpropellable on the ground independently of the car and the rail. Primarily involved here are the feature of a generally upright stabilizer arm pivotally connected to the structure and having an upstanding, roller carrying portion of the arm pivotable by the arm into a stabilized, wheel-gripping contact at about axle height, and the feature of bidirectional power means selectively to pivot the arm into wheel-gripping contact and to return the arm to unpivoted position.