A damping device for reducing pressure oscillations in a combustion system includes at least a portion provided with a first, outer wall, a second, inner wall, an intermediate plate interposed between the first wall and the second wall. This intermediate plate forms a spacer grid to define at least one chamber between said first wall and said second wall, first passages connecting each of said at least one chamber to the inner of the combustion system, and second passages connecting each of said at least one chamber to the outer of the combustion system. The second passages open at the same side of said chambers as the first passages, the second passages have a portion extending parallel to the inner wall. This parallel portion of said second passages is equipped with heat transfer enhancing means.