  Recently (hep-th/9307183) we showed that for the case of the WZW- and the
minimal models fusion can be understood as a certain ring-like tensor product
of the symmetry algebra. In this paper we generalize this analysis to arbitrary
chiral algebras. We define the tensor product of conformal field theory in the
general case and prove that it is associative and symmetric up to equivalence.
We also determine explicitly the action of the chiral algebra on this tensor
product. In the second part of the paper we demonstrate that this framework
provides a powerful tool for calculating restrictions for the fusion rules of
chiral algebras. We exhibit this for the case of the $W_{3}$-algebra and the
$N=1$ and $N=2$ NS superconformal algebras.
