Final answer:
Caviomorph rodents appeared in the fossil record of South America during the Oligocene, like primates, and are classified under Eutherian mammals.
Step-by-step explanation:
Like primates, the mammals that appear in the fossil record of South America in the Oligocene are the caviomorph rodents. These rodents are part of the Eutherian mammals, specifically from the clade Euarchontoglires, which also includes Primates. The Oligocene epoch was a significant time for mammalian evolution and diversification, which included the appearance of various new mammal families.