  The fermionic formula conjectured by Kirillov and Reshetikhin describes the
decomposition (as a module for $U_q(\frak g)$) of a tensor product of multiples
of of fundamental representations $W(m\lambda_i)$ of the corresponding quantum
affine algebras. In this paper, we show that the conjecture is true for the
modules W(m\lambda_i), if $i$ is such that the corresponding simple root occurs
in the highest root of the simple Lie algebra with multiplicity at most 2. In
particular, the conjecture is established for all but a few nodes for the
exceptional algebras.
