Roll is damped by the main dampers - with any roll the suspension must compress, which moves the damper and causes roll damping. On a monoshock car (front monoshock, rear twin shock), there is no roll damping at the front, so it requires the movement at the back of the car (due to diagonal load transfer) to provide any damping.
Sounds to me like worn bushes or drop links. Is the damping reasonably okay (in American car standards) in ride/bump/droop?