  We show that for a locally free action of a simply connected nilpotent Lie
group on a compact manifold, if every real valued cocycle is cohomologous to a
constant cocycle, then the action is parameter rigid. The converse is true if
the action has a dense orbit. Using this, we construct parameter rigid actions
of simply connected nilpotent Lie groups whose Lie algebras admit rational
structures with graduations. This generalizes the results of dos Santos
[Parameter rigid actions of the Heisenberg groups. Ergod. Th. & Dynam. Sys. 27
(2007), 1719-1735] concerning the Heisenberg groups.
