The language of the Nandor, those Telerin Elves who broke from the Great Journey east of the Misty Mountains. As Sindarin became the dominant Elvish tongue of Middle-earth, Nandorin became little-spoken, and by the Third Age, was represented mainly in old place-names and Silvan dialects developed under its influence.
The most extensive posthumously published writing (so far) by J.R.R. Tolkien where he discusses the Nandorin tongue is found in the essay Tengwesta Qenderinwa (TW 2, ca. 1951-1952). Here, we learn that Nandorin was also called Danian (from the leader Dan). As a branch of the Nandor (the Green-elves) turned westward, settling in Ossiriand, Nandorin was divided into West-Danian (also called Ossiriandrin or Ossiriandish, and Laiquenderin) and East-Danian.
In The Lhammas (ca. 1937-1938), Tolkien used different names for these tongues. East Danian is called Leikvian, and the tongue of those who settled in Ossiriand is called Ossiriandic or Ossiriandeb.