The Graeco-Armenian hypothesis originated in 1924 with Holger Pedersen, who noted that agreements between Armenian and Greek lexical cognates are more common than between Armenian and any other Indo-European language.
During the mid-to-late 1920s, Antoine Meillet further investigated morphological and phonological agreements and postulated that the parent languages of Greek and Armenian were dialects in immediate geographical proximity to their parent language, Proto-Indo-European. Meillet's hypothesis became popular in the wake of his Esquisse d'une grammaire comparée de l'arménien classique.
G. R. Solta does not go as far as postulating a Proto-Graeco-Armenian stage but concludes that the lexicon and the morphology clearly make Greek the language that is the most closely related to Armenian.
Eric Hamp supports the Graeco-Armenian thesis and even anticipates a time that "we should speak of Helleno-Armenian" (the postulate of a Graeco-Armenian proto-language). James Clackson is more reserved, considers the evidence of a Graeco-Armenian subgroup to be inconclusive and believes Armenian to be in a larger Graeco-Armeno-Aryan family.
Evaluation of the hypothesis is tied up with the analysis of Indo-European languages, such as Phrygian and languages within the Anatolian subgroup (such as Hittite), many of which are poorly attested, but which were geographically located between the Greek and Armenian-speaking areas, and which would therefore be expected to have traits intermediate between the two. While Greek is attested from very early times, allowing a secure reconstruction of a Proto-Greek language dating to about the 3rd millennium BC, the history of Armenian is opaque where its earliest testimony is the 5th-century Bible translation of Mesrob Mashtots. Armenian has many loanwords showing traces of long language contact with Greek and Indo-Iranian languages; in particular, it is a satem language. Also, although Armenian and Attic (Ancient) Greek share a voiceless aspirate series, they originate from different PIE series (in Armenian from voiceless consonants and in Greek from the voiced aspirates).
Luay Nakhleh, Tandy Warnow, Don Ringe, and Steven N. Evans compared various phylogeny methods and found that five procedures (maximum parsimony, weighted and unweighted maximum compatibility, neighbor joining, and the widely-criticized technique of Russell Gray and Quentin D. Atkinson) support a Graeco-Armenian subgroup.
An interrelated problem is whether there is a "Balkan Indo-European" subgroup of Indo-European, which would consist not only of Greek and Armenian but also Albanian and possibly some dead languages, such as Ancient Macedonian and Phrygian. This has been argued for in research by scholars such as G. Neumann, G. Klingenschmitt, J. Matzinger, J. H. Holst. The Balkan subgroup, in turn, is supported by the lexico-statistical method of Hans J. Holm.