Ape man or Ape-man is a term that people who believe in Evolution (they can be called Evolutionists) use for an entity that had started to evolve, was not fully ape but wasn't fully Human either. Before about 1970 people thought that apes are Animals and vastly inferior to human beings. Today we know that apes (other apes) use tools, think far more than previous generations realised and there isn't such a clear difference between apes and humans. Today we don't use the term ape man so much because we accept that humans are a type of ape. 
Neanderthals were in the past considered ape men but today we believe Neanderthals were human.  Some people think of ape men as Australopithecines.  Australopithecus was a genus of apes/humans and some of that genus gradually evolved into humans. Earlier australopithicines were apelike but some later Australopithecines were more like humans.
- Unfortunately some humans have too much in common with aggressive male common chimps and sadly at least one Tea Party Republican like that was elected to what should be a responsible office. "Jason Priest (Red Lodge) is "a man who threw his daughter like a potato sack, tried to shove his wife down a flight of stairs, fractured her boyfriend’s ribs, and then fought the police officer when he arrived." Priest has been charged with felony assault on a minor and more. Priest ironically chaired the Senate Public Health, Welfare and Safety Committee. See Gun-Toting, Life-Promoting Montana Republican Jailed For Child Abuse.
- Neanderthals Were Fully Human!