The Ani-Men were servants of Arthur Molekevic. He considered them his "children" and they obeyed his commands. Reed Richards correctly deduced that the Ani-Men were composed of "mostly plant" matter. When the Ani-Men first attacked the newly formed Fantastic Four, the group was able to fend off the creatures.
The Ani-Men later appeared in Oregon, when Molekevic again attacked the Fantastic Four and other prodigies of the Baxter Building project in beneath Pinhead Buttes. These Ani-Men had been "enhanced" and "re-shaped" by the Mole Man with "due consideration of" the Fantastic Four's "special abilities". Phineas Mason and his fellow prodigies had determined that the these Ani-Men were fungal in nature. As such they quickly developed a "Mushroom Gun" that destroyed the large group of Ani-Men.