Ungulata: Mammals with hooves. Used here as horses + cows.
from the Latest Cretaceous? (assuming Protungulatum - controversial palcement) or Earliest Paleocene
Characters: $ Stylomastoid foramen opens dorsal to level of cheek teeth [SM98]; Canines reduced [d&C00]; bunodont molars; m3 hypoconulid larger than m2 hypoconulid [d&C00]; astragalus with short, robust head; $? patella rounded or approximately ball-shaped [SM98]; $? distal phalanges spatulate [SM98].
Links: UNGULATA; The Ultimate Ungulate Page; Mammalia/UNGULATA/ungulata.html">Mammalia, Ungulata - Huftiere; ordo Ungulata; Ungulates; Ungulata Catalog (mostly catalog -- a few, very high quality, technical photos); C. Savona-Ventura: Maltese Unglulates.; Salles; Wikipedia (with a very handsome llama); Ungulata Baskin's course notes, with some good links); Paleocene mammals of the world Best on the Web).
References: de Muizon & Cifelli (2000) [d&C00]; Shoshani & McKenna (1998) [SM98]. ATW0.
Comment: The more inclusive Ungulatomorpha (which also includes Zhelestidae and Dinocerata has turned out to be polyphyletic, the zhelestids being stem eutherians convergent with ungulates. The position of the dinocerata is uncertain, we have tentatively placed them in the stem eutherians as well, but more derived than zhelestids. For what it's worth, here's the original entry: Characters: premolars simple [d&C00]; small metaconid on p4 [d&C00]; trigonid cusps sharply conical & well separated (metaconid & paraconid fuse in almost all derived groups) [d&C00]; trigonid open lingually [d&C00]; lower molars with at least weak postcingulid [d&C00]; m2 trigonid slightly wider than talonid (reversed in Zhelestids?) [d&C00]. Links: Basal Ungulatomorpha; g00n1a4.pdf; MESOZOIC MAMMALS; 'basal' Ungulatomorpha, an internet directory: (Best on the Web -- most of the other links are taken from this one); vol3-p18; Welcome to Adobe GoLive 4; Re: Condylarths (TINGAMARRA REVISITED); Ungulate-Like Mammals from the Late Cretaceous of Uzbekistan and ....; The earliest eutherian mammal. References: de Muizon & Cifelli (2000) [d&C00]. ATW021027. links checked ATW040213, updated MAK120321 (links not checked)
Eparctocyona: cows > horses.
Range: from the Late Cretaceous
Phylogeny: Ungulata : Perissodactyla + * : (Arctostylopida + (Triisodontidae + Mesonychia + Cetartiodactyla))) + Bulbulodentata.
Characters: $ paraxonic pes (pes III & IV about equal length) [SM98]; $ lumbricales (see note) muscles reduced or absent [SM98] ; $ "incus crus breve is longer than crus longum" (beats me! please email if you know what this one means) [SM98].
Note:  the m. lumbricales are intrinsic muscles of the hands & feet originating in the palm and inserting on the radial side of the metacarpals (or -tarsals). They are responsible for flexing the digits at the metacarpo-phalangeal joint and extending the digits at the interphalangeal joints for digits II-V. This undoubtedly explains why cows and whales do not use hand puppets or wave "bye-bye."  I've seen various references equating Eparctocyona with Cetartiodactyla, presumably from folks who have forgotten the South American archaic ungulates and the like. Cetartiodactyla is, as the name suggests, the crown group cows + whales. This is the -- much more inclusive -- stem group: cows > horses.
References: Shoshani & McKenna (1998) [SM98]. ATW060320
Arctostylopida: Allostylops, Arctostylops, Asiostylops, Bothriostylops, Gashatostylops, Kazachostylops, Palaeostylops, Sinostylops.
Range: Late Paleocene to Early Eocene of China, Mongolia, Central Asia & North America
Phylogeny: Eparctocyona :: (Triisodontidae + (Mesonychia + Cetartiodactyla)) + *.
Characters: molars with relatively hypsodont crowns, especially buccally [Z04]; buccal wall of crown featureless, without buccal cingulum or folds at ectoloph cusps [Z04]; crown elongate & longer buccally than lingually [Z04]; protocone & pseudohypocone small & closely appressed [Z04]; distal cingulum tall & lophate [Z04]; crown inflated at lingual basal margin [Z04]; specialists in fibrous and/or abrasive vegetation [Z04].
Links: Arctostylopida Mikko); pal4 (list); Species Skull Ht Lt Wt Time Range Acama probably Acamana U ... dates & locations); AN EARLY EOCENE ARCTOSTYLOPID (Mammalia- ARCTOSTYLOPIDA) FROM THE ... Zack, 2004).
Note: These are early mammals of rather uncertain affinities. It is by no means certain that they are even ungulates [Z04].
References: Zack (2004) [Z04]. ATW060320.
Triisodontidae: Eoconodon, Triisodon.
Range: early to middle Paleocene of North America.
By far the largest mammals in the early Paleocene. Massive jaws; strong canine teeth (at least some degree of carnivory); heavily built, blunt, crushing cheek teeth; flattened claws instead of nails.
Links: Paleocene mammals of the world; Paleocene mammals of the world; Transitional Vertebrate Fossils FAQ: Part 2B. ATW010512.
Mesonychia: Dissacus, Harpagolestes, Mesonyx.
Range: Middle Paleocene to Early Oligocene.
Characters: Medium to large-sized, possibly dominant predators or scavengers of mid-Paleocene. Molars modified to generate vertical shear; lower molars thin and blade-like, with carnassial notches (but no true carnassials); protoconid dominates lower molars, with paraconid anterior and metaconid reduced; talonid low, with loss of hypoconulid, entoconulid, & talonid basin; talonid dominated by hypoconid & crista; upper molars triangular, with extension of parastyle & metastyle, reduction of paraconule & metaconule; all molars laterally compressed; molars often blunt, shearing or crushing surfaces; large temporal fossa & high sagittal crest; metapodials well-integrated; hoofed feet; primitively plantigrade (?) or digitigrade.
Links: The time of origin of the Cetacea; Skull of a new Mesonychid; Paleocene mammals of the world; Postcranial skeleton of Pachyaena; gate.pdf; 8gate.pdf; Untitled Document; Mesonychia after O'Leary, 1998a, b; TIME OF ORIGIN OF MESONYCHIA; The Emergence of Whales, Chp. 5; Whales, not whippos, part I: Nature; Science News: Hippo-Whale Link; 413277aa.doc; Evidence for a Paleocene Evolutionary Radiation; Mesonychia after O'Leary, 1998a, b; NCRV - Natuur - Walking With Beasts - Mesonychia; The Mitochondrial Genome of the Sperm Whale and a New Molecular ....; Wikipedia. ATW030628.
Bulbulodentata: stem group including the paraphyletic "Mioclaenidae" as well as the Periptychidae.
Characters: premolars "swollen";
Links: Bulbulodentata Mikko); Species Skull Ht Lt Wt Time Range Acama probably Acamana U ... time & place); de Muizon & Cifelli important article with full text pdf -- Best on the Web). ATW021224.
Hyopsodontidae: Hyopsodon, Litomylus, Louisina, Paschatherium.
Range: Late Paleocene to Late Eocene of Europe, Africa, North America & ?China. Probably not South America. Most common in North America.
Phylogeny: Bulbulodentata : Meridiungulata + *.
Characters: insectivore-like animals with arboreal capabilities; hypocone large; parastylar lobe present and larger on M3 than M2; primitively, preparacrista & postmetacrista oriented mesiodistally; trigonid relatively open lingually; paraconid not appressed to metaconid; entoconid large; hypoconid well developed.
Image: Hyopsodus from Paleocene Mammals of the World, which credits Savage, RJG & MR Long (1986), Mammal Evolution. An Illustrated Guide. British Museum (Natural History).
Notes: Recent work suggests that this may be a synonym for Mioclaenidae, a well-known condylarth group. In addition, some hyopsodonts the group may be polyphyletic) may be the sister group, or even include, the "Afrotherian" clade of (at least) elephant shrews (Macroscelidea) [Z+05]. Note that this has resonances in the some of the web citations below.
Links: Hyopsodontidae Mikko); Untitled Document suggesting a relationship with elephant shrews and elephants); Bootstrap method with heuristic search-; Conddylarths (Steve & Casey's); Untitled (Czech); Turtles (and Afrotheria) (long); The "condylarths" (archaic Ungulata, Mammalia) from the early ...; Main Page Ben Berger's page, which was long extinct, seems to have been resurrected); Paleocene mammals of the world suggesting a link with insectivores); Turtles (and Afrotheria) (long) same); Volume 31 No. 2, abstract of Robinson article showing odd evolutionary pattern); Институт проблем экологии и эволюции имени А. Н. Северцова.(Russian: abstract of Agadzhanian article arguing hyopsodonts are ancestral to tapirs and indricotheres).
References: Zack et al. (2005) [Z+05]. ATW030714.