Neanderthals were
horticulturalists
agriculturalists
foragers
pastoralists

Foragers

Explanation:

The Neanderthals were a hominid species that was living in Eurasia and dominating the area until the migration of Homo sapiens to its territory. These hominids were foragers. Their lifestyle was based on hunting animals to survive, and often they moved along the animals they hunted as they were migration from one place to another. They were not practicing agriculture, or rarely spent longer period of time at one place as they were not going to be able to sustain themselves.