Integrability and chaos are antinomic concepts [1]. This is specially clear for classical dynamics, where “complete integrability” means the existence of tori. It is also apparent in Poincare’s classification [2] into “integrable” and “non-integrable” systems. As was shown by the KAM theory [1,3], non-integrability leads to the appearance of random trajectories. In this paper, we summarize our work on “large Poincare systems” (hereafter refered to as LPS), i.e., the systems which have a continuous spectrum and continuous sets of resonances. This implies that in LPS, almost all trajectories become random. LPS are of special interest as they have a wide range of generality. The concept of LPS is also valid in quantum mechanics and it includes the systems studied in kinetic theory, as well as problems such as radiation damping, interacting fields and so on.