Let \(g\) be a polynomial sequence of translations of a compact nilmanfold \(X\) and let \(A\) be the group generated by the elements of \(g\). It is shown that for almost all points \(x\in X\), the closures of orbits of points \(x\) under the action of \(g\) are congruent to the connected components of the closure of orbits of the points \(x\) under the action of \(A\).