  We investigate free non-local massless and massive scalar field on deSitter
(dS) space-time. We compute the propagator for the non-local scalar field for
the corresponding theories on flat and deSitter space-times. It is seen that
for the non-local theory, the massless limit of massive propagator is smooth
for both flat and deSitter. Moreover, this limit matches exactly with the
massless propagator of the non-local scalar field for both flat and deSitter
space-time. The propagator is seen to respect dS invariance. Furthermore,
investigations of the non-local Green's function on deSitter for large
time-like separation shows that the propagator has no infrared divergences. The
dangerous infrared $\log$-divergent contributions which arise is local massless
theories are absent in the corresponding non-local version. Lack of infrared
divergences in the propagator hints at the strong role non-localities may play
in the dS infrared physics. This study suggest that non-locality can cure IR
issues in deSitter.
