  We present scattering of stringy states of closed bosonic string compactified
on d-dimensional torus. We focus our attention on scattering of moduli and
gauge bosons. These states appear when massless excitations such as graviton
and antisymmetric tensor field of the uncompactified theory are dimensionally
reduced to lower dimension. The toroidally compactified theory is endowed with
the T-duality symmetry, O(d,d). Therefore, it is expected that the amplitude
for scattering of such states will be $T$-duality invariant. The formalism of
Kawai-Llewelen-Tye is adopted and appropriately tailored to construct the
vertex operators of moduli and gauge bosons. It is shown, in our approach, that
N-point amplitude is T-duality invariant. We present illustrative examples for
the four point amplitude to explicitly demonstrate the economy of our formalism
when three spatial dimensions are compactified on three dimensional torus. It
is also shown that if we construct an amplitude with a set of 'initial'
backgrounds, the T-duality operation transforms it to an amplitude associated
with another set backgrounds. We propose a modified version of KLT approach to
construct vertex operators for nonabelian massless gauge bosons which appear in
certain compactification schemes.
