MPEJ Volume 8, No. 1, 13 pp. Received: Feb 13, 2002. Accepted: Feb 21, 2002. Bambusi D., Gaeta G.: On persistence of invariant tori and a theorem by Nekhoroshev ABSTRACT: We give a proof of a theorem by N.N. Nekhoroshev concerning Hamiltonian systems with $n$ degrees of freedom and $s$ integrals of motion in involution, where $1 \leq s \leq n$. Such a theorem ensures persistence of $s$-dimensional invariant tori under suitable nondegeneracy conditions generalizing Poincar\'e's condition on the Floquet multipliers. http://www.maia.ub.es/mpej/Vol/8/1.ps http://www.ma.utexas.edu/mpej/Vol/8/1.ps http://mpej.unige.ch/mpej/Vol/8/1.ps