  To any connected and simply connected nilpotent Lie group N, one can
associate its group of affine transformations Aff(N). In this paper, we study
simply transitive actions of a given nilpotent Lie group G on another nilpotent
Lie group N, via such affine transformations. We succeed in translating the
existence question of such a simply transitive affine action to a corresponding
question on the Lie algebra level. As an example of the possible use of this
translation, we then consider the case where dim(G)=dim(N) less than 6.
  Finally, we specialize to the case of abelian simply transitive affine
actions on a given connected and simply connected nilpotent Lie group. It turns
out that such a simply transitive abelian affine action on N corresponds to a
particular Lie compatible bilinear product on the Lie algebra of N, which we
call an LR-structure.
