  The intrinsic multivaluedness of interaction process, revealed in Part I of
this series of papers, is interpreted as the origin of the true dynamical (in
particular, quantum) chaos. The latter is causally deduced as unceasing series
of transitions, dynamically probabilistic by their origin, between the equally
real, but incompatible 'realisations' (modes of interaction) of a system. The
obtained set of realisations form the causally derived, intrinsically complete
"space of events" providing the crucial extension of the notion of probability
and the method of its first-principle calculation. The fundamental dynamic
uncertainty thus revealed is specified for Hamiltonian quantum systems and
applied to quantum chaos description in periodically perturbed systems. The
ordinary semiclassical transition in our quantum-mechanical results leads to
exact reproduction of the main features of chaotic behaviour of the system
known from classical mechanics, which permits one to "re-establish" the
correspondence principle for chaotic systems (inevitably lost in any their
conventional, single-valued description). The causal dynamical randomness in
the extended quantum mechanics is not restricted, however, to semiclassical
conditions and generically occurs also in essentially quantum regimes, even
though partial "quantum suppression of chaos" does exist and is specified in
our description, as well as other particular types of the quantum (truly)
chaotic behaviour.
