  The status of classical stability in higher-derivative systems is still
subject to discussions. In this note, we argue that, contrary to general
belief, many higher-derivative systems are classically stable. The main tool to
see this property are Nekhoroshev's estimates relying on the action-angle
formulation of classical mechanics. The latter formulation can be reached
provided the Hamiltonian is separable, which is the case for higher-derivative
harmonic oscillators. The Pais-Uhlenbeck oscillators appear to be the only type
of higher-derivative harmonic oscillator with stable classical dynamics. A wide
class of interaction potentials can even be added that preserve classical
stability. Adiabatic invariants are built in the case of a Pais-Uhlenbeck
oscillator slowly changing in time; it is shown indeed that the dynamical
stability is not jeopardised by the time-dependent perturbation.
