_Description._--Size medium to large; skull becoming angular and rugose with age, and tending towards platycephaly and dorso-ventral compression; zygomata stout, each bearing platelike expansion at anterolateral angle into which anterior end of jugal becomes morticed; breadth across zygomata great relative to length of skull; rostrum relatively broad; squamosals expanding medially with age eventually growing over lateral parts of parietals, and sometimes also expanding laterally displacing postglenoid notch; sagittal crest well developed in adults of both sexes, but especially high and bladelike in males; lambdoidal crest prominent in all but young animals, having dorsal outline broadly convex posteriorly in most species but strongly sinuous in _gymnurus_-group; enamel plate on posterior wall of P4 absent; enamel plates present only on anterior walls of M1 and M2; M3 variform in occlusal shape (as described in species account), either subtriangular (_gymnurus_-group), quadriform or obcordate (_castanops_-group, with exceptions as noted before); lateral plates of M3 usually present in all species, labial plate approximately as long as lingual plate in _gymnurus_-group (like that in subgenus _Pappogeomys_) or distinctly shorter in _castanops_-group (labial plate scarcely extending beyond border of labial re-entrant fold); one or both lateral plates tending to disappear with wear in _castanops_-group, with lingual plate usually disappearing first; breadth across angular processes clearly more than breadth across zygomatic processes, especially in _gymnurus_-group. _Remarks._--In the species of the _castanops_-group the skulls can be spoken of as generalized and the least platycephalic of the subgenus. Indeed, the species of the _castanops_-group are hardly more specialized in this respect than is the subgenus _Pappogeomys_. In these skulls the breadth across the squamosal processes is less than that across the zygomatic arches, although the two dimensions are almost equal in some examples of _P. merriami_ of the _castanops_-group (where squamosal breadth varies from 85 to 98% of zygomatic breadth). In the species having marked platycephalic skulls (_gymnurus_ species-group) the breadth across the squamosal processes equals or exceeds the breadth across the zygomatic arches (squamosal breadth rarely 97 to 99% of zygomatic breadth), except in _P. zinseri_ and _P. tylorhinus zodius_.