  We consider pairs (V,H) of subgroups of a connected unipotent complex Lie
group G for which the induced VxH-action on G by multiplication from the left
and from the right is free. We prove that this action is proper if the Lie
algebra g of G is 3-step nilpotent. If g is 2-step nilpotent then there is a
global slice of the action that is isomorphic to C^n. Furthermore, a global
slice isomorphic to C^n exists if dim V = 1 = dim H or dim V = 1 and g is
3-step nilpotent. We give an explicit example of a 3-step nilpotent Lie group
and a pair of 2-dimensional subgroups such that the induced action is proper
but the corresponding geometric quotient is not affine.
