|Ocucajea (top), S. muizoni (below)|
Uhen et al. 2011
Supayacetus is known from the holotype MUSM 1465, a partial skeleton. As Ocucajea, it was collected in the Archaeocete Valley site, from the Paracas Formation of the Pisco Basin about . It was named by Uhen et al. 2011 and the type species S. muizoni honours palaeontologist Christian de Muizon who has contributed considerably to Peruvian palaeontology.
Distinguishing characters of Supayacetus include: a T-shaped manubrium with a rod-shaped process; cheek teeth with accessory denticles; a broad scapula with a large infraspinous fossa; humerus with large and hemispherical head, well-defined proximal tuberosities, a long deltopectoral crest, and a broad shaft. Compared to other basilosaurids, Supayacetus is larger than Protocetus but its skull and vertebrae are smaller than in other basilosaurids. 
- Uhen, Mark D.; Pyenson, Nicholas D.; Devries, Thomas J.; Urbina, Mario; Renne, Paul R. (2011). "New Middle Eocene Whales from the Pisco Basin of Peru". Journal of Paleontology. 85 (5): 955–69. doi:10.1666/10-162.1. hdl:10088/17509. OCLC 802202947.CS1 maint: ref=harv (link)