  We study conservation laws of a general class of quantum many-body systems
subjected to an external time dependent quasi-periodic driving. We show that,
when the frequency of the driving is large enough or the strength of the
driving is small enough, the system exhibits a prethermal state for stretched
exponentially long times in the perturbative parameter. Moreover, we prove the
quasi-conservation of the constants of motion of the unperturbed Hamiltonian
and we analyze their physical meaning in examples of relevance to condensed
matter and statistical physics.
