A homomorphism from an oriented graph G to an oriented graph H is an arc-preserving mapping from V(G) to V(H), that is (x)(y) is an arc in H whenever xy is an arc in G. The oriented chromatic number of G is the minimum order of an oriented graph H such that G has a homomorphism to H. The oriented chromatic index of G is the minimum order of an oriented graph H such that the line-digraph of G has a homomorphism to H. In this paper, we determine for every the oriented chromatic number and the oriented chromatic index of the class of oriented outerplanar graphs with girth at least