  This paper is an extended version of our previous short letter \cite{ZG2} and
is attempted to give a detailed account for the results presented in that
paper. Let $U_q({\cal G}^{(1)})$ be the quantized nontwisted affine Lie algebra
and $U_q({\cal G})$ be the corresponding quantum simple Lie algebra. Using the
previous obtained universal $R$-matrix for $U_q(A_1^{(1)})$ and
$U_q(A_2^{(1)})$, we determine the explicitly spectral-dependent universal
$R$-matrix for $U_q(A_1)$ and $U_q(A_2)$. We apply these spectral-dependent
universal $R$-matrix to some concrete representations. We then reproduce the
well-known results for the fundamental representations and we are also able to
derive for the first time the extreamly explicit and compact formula of the
spectral-dependent $R$-matrix for the adjoint representation of $U_q(A_2)$, the
simplest nontrival case when the tensor product of the representations is {\em
not} multiplicity-free.
