  We investigate a scenario of photons scattering by electrons within a
relativistic outflow. The outflow is composed of discrete shells with different
speeds. One shell emits radiation for a short duration. Some of this radiation
is scattered by the shell(s) behind. We calculate in a simple two-shell model
the observed scattered flux density as a function of the observed primary flux
density, the normalized arrival time delay between the two emission components,
the Lorentz factor ratio of the two shells and the scattering shell's optical
depth. Thomson scattering in a cold shell and inverse Compton scattering in a
hot shell are both considered. The results of our calculations are applied to
the Gamma-Ray Bursts and the afterglows. We find that the scattered flux from a
cold slower shell is small and likely to be detected only for those bursts with
very weak afterglows. A hot scattering shell could give rise to a scattered
emission as bright as the X-ray shallow decay component detected in many
bursts, on a condition that the isotropically equivalent total energy carried
by the hot electrons is large, $\sim 10^{52-56}$ erg. The scattered emission
from a faster shell could appear as a late short $\gamma$-ray/MeV flash or
become part of the prompt emission depending on the delay of the ejection of
the shell.
