A　proper　edge　coloring　of　a　graph　G　is　called　acyclic　if　there　is　no　2-colored　cycle　in　G.　The　acyclic　edge　chromatic　number　of　G,　denoted　by　7(G),　is　the　least　number　of　colors　in　an　acyclic　edge　coloring　of　G.　In　this　paper,　we　determine　completely　the　acyclic　edge　chromatic　number　of　outerplanar　graphs.　The　proof　is　constructive　and　supplies　a　polynomial　time　algorithm　to　acyclically　color　the　edges　of　any　outerplanar　graph　G　using　chi(a)＇(G)　colors.　(C)　2009　Wiley　Periodicals.　Inc.　J　Graph　Theory　64:　22-36,　2010