There is a lot of academic debate about whether the Yuezhi are to be considered Indo-Iranian or Tocharian, or even turcic (although the arguments for the latter claim are rather weak). Given how many historians make the connection between the Yuezhi and Tocharians, I would perhaps not call it controversial. In fact, there has been some arguments made that the name Yuezhi, which in old chinese sounds something like "Ngwatieg" may actually be a chinese attmpt at rendering the word "tokhar". Further, greaco-roman sources mention the in the invasion of Baktria by nomads a number of tribes, among them one called Tocharii, and this invasion is in chinese sources ascribed to the Yuezhi. This too seems to link the Yuezhi to the Tocharians. That the Kushanas, whom the chinese still called Yuezhi, used Tocharian in some official texts also points this way, and Baktria later bacame known as Tokharistan.
However, one of the more plausible explanations is that the Yuezhi contained a large contingent of Tocharian speakers, but were not exclusively Tocharian, much like the Xiongnu is often described as an altaic people, altough some chinese sources describe them as red haired, which seems to imply the inclusion of Indo-european peoples within their ranks. Genreally, steppe tribal names often do not refer to a specific ethnic group, but is more of a collective name for all the tribes within a larger federation, much like the Huns were probably made up both of Turkic, Iranian and Scythian/Sarmatian people, and the Mongols that invaded Europe in the 13th century in fact contained pepole of various ethnic and linguistic origin. The Yuezhi most likely contained several diverse ethnic and linguistic groups, but it does not seem implausible that a subtsantial part of them were Tocharian, and the Tocahrian theory seems to be the most prevalent veiw among scholars today.
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