  In this paper, we consider a Diophantine quasi-periodic time-dependent
analytic perturbation of a convex integrable Hamiltonian system, and we prove a
result of stability of the action variables for an exponentially long interval
of time. This extends known results for periodic time-dependent perturbations,
and partly solves a long standing conjecture of Chirikov and Lochak. We also
obtain improved stability estimates close to resonances or far away from
resonances, and a more general result without any Diophantine condition.
