  In this paper we study affine and bilinear systems on Lie groups. We show
that there is an intrinsic connection between the solutions of both systems.
Such relation allows us to obtain some preliminary controllability results of
affne systems on compact and solvable Lie groups. We also show that the
controllability property of bilinear systems is very restricted and may only be
achieved if the state space G is an Euclidean space.
