  In this paper we introduce the sheaf of stratified Whitney jets of Gevrey
order on the subanalytic site relative to a real analytic manifold X. Then we
define stratified ultradistributions of Beurling and Roumieu type on X. In the
end, by means of stratified ultradistributions, we define tempered-stratified
ultradistributions and we prove two results. First, if X is a real surface, the
tempered-stratified ultradistributions define a sheaf on the subanalytic site
relative to X. Second, the tempered-stratified ultradistributions on the
complementary of a 1-regular closed subset of X coincide with the sections of
the presheaf of tempered ultradistributions.
