A process for manufacturing a cylindrical composite component comprises includes producing a fibrous texture in the form of a strip by three-dimensional or multi-layer weaving, winding the fibrous texture on several superimposed lathes on a mandrel with a profile corresponding to that of the component to be manufactured so as to form a fibrous preform, densifying the fibrous preform by a matrix. When the fibrous texture is wound on the mandrel, a web including a fugitive material filled with carbon nanotubes is interposed between the adjacent turns of the fibrous texture.