  In this paper we study the propagator of a vector fields on a euclidean
maximally-symmetric background in arbitrary space-time dimensions. We study two
cases of interest: Massive and massless vector fields. In each case we computed
the propagator of the vector fields on euclidean deSitter background, isolating
the transverse and longitudinal part. In both case of massive and massless
vector fields, the short distance limit of the full propagator agrees with the
flat space-time propagator. In the case of massive propagator, the transverse
part has a well defined massless limit, and in this limit it goes to the
transverse propagator for the massless fields. The transverse propagator for
antipodal point separation is nonzero and negative, but vanishes in the flat
space-time limit (Ricci scalar going to zero). The longitudinal part of the
massive propagator diverges as $1/m^2$, where $m$ is the mass of the field. The
longitudinal part of the massless propagator is gauge dependent and in
particular is proportional to the gauge parameter used in the gauge fixing
condition. It vanishes in the Landau gauge. Comparison with the past literature
is made.
