  We study Zamolodchikov algebras whose commutation relations are described by
Belavin matrices defining a solution of the Yang-Baxter equation (Belavin
$R$-matrices). Homomorphisms of Zamolodchikov algebras into dynamical algebras
with exchange relations and also of algebras with exchange relations into
Zamolodchikov algebras are constructed. It turns out that the structure of
these algebras with exchange relations depends substantially on the primitive
$n$th root of unity entering the definition of Belavin $R$-matrices.
