**Abstract: **
Let $H(t):=-\partial_x^2+x^2+V(\omega t) $ acting in $L^2(\R)$
denote the Hamiltonian of a $T:=2\pi/\omega$-periodically driven harmonic
oscillator and $K:=-i\partial_t+H(t)$ the corresponding Floquet
Hamiltonian which acts in $L^2( T S^1)\otimes L^2(\R)$. We shall give
sufficient condition on the frequency $\omega$ and the size and the
regularity of $V$ to insure that $K$ is pure point, i.e. this system is
stable. Work in progress with M. Vittot.