  Perturbation of gravitational fields may be decomposed into scalar,vector and
tensor components.In this paper we concern with the evolution of tensor mode
perturbations in a spatially closed deSitter background of RW form. It may be
thought as gravitional waves in a classical description. The chosen background
has the advantage of to be maximally extended and symmetric. The spatially flat
models commonly emerge from inflationary scenarios are not completely
extended.We first derive the general weak field equations.Then the form of the
field equations in two special cases, planar and spherical waves are obtained
and their solutions are presented. We conclued with discussing the significance
of the results and their implications.
