The　Wiener　index　W(G)　and　the　edge-Wiener　index　W-e(G)　of　a　graph　G　are　defined　as　the　sum　of　all　distances　between　pairs　of　vertices　in　a　graph　G　and　the　sum　of　all　distances　between　pairs　of　edges　in　G,　respectively.　The　Wiener　index,　due　to　its　correlation　with　a　large　number　of　physico-chemical　properties　of　organic　molecules　and　its　interesting　and　non-trivial　mathematical　properties,　has　been　extensively　studied　in　both　theoretical　and　chemical　literature.　The　edge-Wiener　index　of　G　is　nothing　but　the　Wiener　index　of　the　line　graph　of　G.　The　concept　of　line　graph　has　been　found　various　applications　in　chemical　research.　In　this　paper,　we　show　that　if　G　is　a　catacondensed　hexagonal　system　with　h　hexagons　and　has　t　linear　segments　S-1,　S-2,　,S-t　of　lengths　l(S-i)　=　l(i)(1　＜=　i　＜=　t),　then　W-e(G)　=　25/16W(G)　+　1/16(120h(2)　+　94h　+　29)　-　1/4　Sigma(t)(i=1)(l(i)　-　1)(2).　Our　main　result　reduces　the　problems　on　the　edge-Wiener　index　to　those　on　the　Wiener　index　in　the　catacondensed　hexagonal　systems,　which　makes　the　former　ones　easier.　(C)　2015　Elsevier　Inc.　All　rights　reserved.