  The dynamical structure factor $S(q,\omega)$ of the K-component (K = 2,3,4)
spin chain with the 1/r^2 exchange is derived exactly at zero temperature for
arbitrary size of the system. The result is interpreted in terms of a free
quasi-particle picture which is generalization of the spinon picture in the
SU(2) case; the excited states consist of K quasi-particles each of which is
characterized by a set of K-1 quantum numbers. Divergent singularities of
$S(q,\omega)$ at the spectral edges are derived analytically. The analytic
result is checked numerically for finite systems.
