  We generalize permutative representations of the Cuntz algebras for the \cka\
$\coa$ for any $A$. We characterize cyclic permutative representations by
notions of cycle and chain, and show their existence and uniqueness. We show
necessary and sufficient conditions for their irreducibility and equivalence.
In consequence, we have a complete classification of permutative
representations of $\coa$. Furthermore we show decomposition formulae and that
the uniqueness of irreducible decomposition holds for permutative
representation.
