  We show that a nonlinear dynamical system in Poincare'-Dulac normal form (in
$\R^n$) can be seen as a constrained linear system; the constraints are given
by the resonance conditions satisfied by the spectrum of (the linear part of)
the system and identify a naturally invariant manifold for the flow of the
``parent'' linear system. The parent system is finite dimensional if the
spectrum satisfies only a finite number of resonance conditions, as implied
e.g. by the Poincare' condition. In this case our result can be used to
integrate resonant normal forms, and sheds light on the geometry behind the
classical integration method of Horn, Lyapounov and Dulac.
