Yet another heresy today.
A proposal for a shift in common usage is presented here.
Wikipedia reports:
“Pelycosauria is a paraphyletic taxon because it excludes the therapsids. For that reason, the term is sometimes avoided by proponents of a strict cladistic approach. Eupelycosauria is used to designate the clade that includes most Pelycosaurs, along with the Therapsida and the Mammals. Pelycosaurs ‘consist of all synapsids except for the therapsids and their descendants.'”
- Order Pelycosauria*
- Family Eothyrididae
- Family Caseidae
- Family Varanopidae
- Family Ophiacodontidae
- Family Edaphosauridae
- Family Sphenacodontidae
Unfortunately
Eothyridae and Caseidae are not synapsids, but synapsid mimics, as recovered by the large reptile tree (LRT, 1173 taxa; subset (Fig.1), first documented about seven years ago here.
Moreover
several former varanopids now nest as Pro- or Protodiapsids retaining a single temporal opening, in the lineage of Diapsida, not Mammalia. These include:
- Heleosaurus
- Mycterosaurus
- Nikkasaurus
- Mesenosaurus
- Niaftasuchus
- Archaeovenator
- Orovenator
- Pyozia
- Broomia
- Milleropsis
- Erpetonyx
Given all these shake-ups
if we restrict members of the clade Pelycosauria to just Pantelosaurus, Haptodus, their last common ancestor and all descendants (including Edaphosauridae + Sphenacodontidae) then we shall have a monophyletic Pelycosauria.

Figure 1. Basal Synapsida. A monophyletic Pelycosauria is present (in green) if we can accept the changes suggested in the text.
What about the Eupelycosauria (Kemp 1982)?
If caseids are considered the proximal outgroup taxa to the Eupelycosauria, or simply not part of the definition, then the remaining taxa are identical to those earlier considered members of the Synapsida. Thus Eupelycosauria is a junior synonym for the earlier clade name, Synapsida.
Re: Tetraceratops
As we learned earlier here, due to taxon exclusion Laurin and Reisz 1990, 1996) considered Tetraceratops the oldest known therapsid. In the LRT Tetraceratops nests with Tseajaia, a limnoscelid, far from the Synapsida.
References
Kemp TS 1982.Mammal-like Reptiles and the Origin of Mammals1-363
Laurin M and Reisz RR 1990. Tetraceratopsis the oldest known therapsid. Nature 345: 249-250.
Laurin M and Reisz RR. 1996.The osteology and relationships of Tetraceratops insignis,is the oldest known therapsid. Journal of Vertebrate Paleontology 16: 95-102.
Laurin M and Reisz, RR 1997. Autapomorphies of the main clades of synapsids – Tree of Life Web Project.