  Let X be a vector field on a compact connected manifold M. An important
question in dynamical systems is to know when a function g:M -> R is a
coboundary for the flow generated by X, i.e. when there exists a function f:
M->R such that Xf=g. In this article we investigate this question for nilflows
on nilmanifolds. We show that there exists countably many independent Schwartz
distributions D_n such that any sufficiently smooth function g is a coboundary
iff it belongs to the kernel of all the distributions D_n.
