\abstract
A mathematical notion of interaction is
introduced for noncommutative dynamical systems,
i.e., for one parameter groups of automorphisms
of $\Cal B(H)$ endowed with a certain causal structure.
With any interaction there is a well-defined
``state of the past" and a well-defined
``state of the future".
We describe the construction of many
interactions involving cocycle perturbations
of the CAR/CCR flows and
show that they are nontrivial.  The key element
in the proof of nontriviality
is an inequality which relates the
eigenvalue lists of the ``past" and ``future" states
to the norm of a linear functional on
a certain $C^*$-algebra.
\endabstract