  Using U_q(a_n^(1))- and U_q(a_2n^(2))-invariant R-matrices we construct exact
S-matrices in two-dimensional space-time. These are conjectured to describe the
scattering of solitons in affine Toda field theories. In order to find the
spectrum of soliton bound states we examine the pole structure of these
S-matrices in detail. We also construct the S-matrices for all scattering
processes involving scalar bound states. In the last part of this paper we
discuss the connection of these S-matrices with minimal N=1 and N=2
supersymmetric S-matrices. In particular we comment on the folding from N=2 to
N=1 theories.
