Phylogenetic systematics, first used for reconstructing biological evolution, has become popular in historical linguistics for reconstructing the development of language families. This dissertation tests three approaches to phylogenetic analysis of the Ancient Greek dialects in order to determine which one best handles borrowing. For character weighting, only reweighting characters according to their CI (consistency index) improved the resolution of the final tree while still giving a plausible tree topology. NeighborNet captured the basic tree topology, but was not able to capture certain important types of borrowing. Combining taxa through a preliminary cluster analysis also produced a single tree with a plausible tree topology. However, all of these methods fail to capture a circular dialect continuum among the Greek dialects, indicating that tree methods alone cannot capture some important types of linguistic development.