Men of the Vales of Anduin is a frustratingly vague term used in The Lord of the Rings to refer (apparently) to any and/or all human inhabitants, of any time, of the Upper Anduin Vales of Rhovanion. We know certainly that Men had passed westward through this region in the First Age, at least the ancestors of the Edain, so it is possible – even probable – that some of their kinsmen had settled there and survived into later ages. However, the earliest specific mentions go back only as far as the first part of the Third Age (when they were said to have acknowledged the rule of Gondor at its height). The Éothéod also lived in the Northern Anduin Vales for some time (about six and a half centuries), so they too could be so labeled, but it seems clear that they are considered to be a transient group, distinct from other "Men of the Vales of Anduin".
MERP[]
In MERP, the Anduin River Culture, also known as Nenedain (S. "Men [of the] Waters") or Nenemardain, were an early Mannish culture in the Northern Anduin Vales. These men were believed to have descended from wandering Lintanoi and eastern kinsmen of the Beorians and Hadorians, who had either never crossed the Hithaeglir or had returned to Rhovanion to escape the growing Númenórean hegemony, and who had settled along the upper waters of the Great River (hence the name Nenedain). The Woodmen, Mangeras, and Beornings, and possibly the Lake-men and Dale-men, were their descendants.