[en] A solution of the gravitational field equations is found by using an axially symmetric metric which is asymptotically a de Sitter space metric. The general approach of Bondi, van der Burg, and Metzner as applied to the asymptotic flat-space case is used and a search is made for the necessary conditions for gravitational radiation in asymptotic de Sitter space. It is found that the character of the gravitational radiation, if it exists at all, is considerably different from that obtained in the case of asymptotic flat space. (author)