Which ancient mammals were probably ancestors of perissodactyls?

Perissodactyls were likely derived from the Condylarthra, a group of unspecialized, largely herbivorous mammals that were abundant in Europe and North America during the Paleocene Epoch (approximately 65.5 million to 55.8 million years ago).1

These ancestral condylarths were somewhat carnivore-like in appearance, with some larger species reaching the size of tapirs. While their limbs were relatively short and primitive, they exhibited early signs of the traits that would characterize later ungulates: the third toe was somewhat enlarged, and their phalanges ended in hooves. Additionally, they possessed a full complement of teeth, featuring some specialization of bunodont molars suitable for a herbivorous diet.1