Probably associated with the characters of the order, as given above, are the connection of pectoral girdle with skull, and the presence of a tympanic membrane, the stapes functioning in both sound-transmission and palatoquadrate suspension. Family HESPEROHERPETONIDAE Orbits and foramen magnum unusually large in correlation with reduced size of animal; squamosal forming posterior margin of orbit; circumorbital series absent (except for postorbital); sensory pits on squamosal and frontal. Characters defining the family are evidently the more specialized cranial features, which probably evolved during Mississippian and early Pennsylvanian times. The definition of the genus and species may be left to rest upon Peabody's (1958) original description and the present account, until the discovery of other members of the family gives reason for making further distinctions. SUMMARY _Hesperoherpeton garnettense_ Peabody (1958), based on a scapulocoracoid and part of a vertebra, was originally placed in the order Anthracosauria, suborder Embolomeri, family Cricotidae. A new skeleton from the type locality near Garnett, Kansas (Rock Lake shale, Stanton formation, Upper Pennsylvanian), shows that the animal has the following rhipidistian characters: Large notochordal canal below foramen magnum, otico-occipital block separate from ethmosphenoid, postaxial processes on three axial bones of forelimb, pectoral girdle (probably) articulated with tabular. Nevertheless, _Hesperoherpeton_ has short digits, an anthracosaurian type of pectoral girdle, an otic rather than spiracular notch, nostrils separate from the mouth, and vertebrae in which the intercentrum is U-shaped and the pleurocentra large but paired. The stapes reaches the quadrate. _Hesperoherpeton_ is placed in a new order, PLESIOPODA, on the basis of the characters stated above, and a new family, HESPEROHERPETONIDAE. Specialized characters of the family include: Reduction of circumorbital bones, bringing the squamosal to the edge of the orbit, loss of certain bones of the temporal region, and relative enlargement of the orbits and foramen magnum, in correlation with the diminutive size of the animal. The structural characters of _Hesperoherpeton_ suggest to us that it lived in the shallow, weedy margins of lagoons, rested with its head partly out of water, and normally did not walk on land. LITERATURE CITED EATON, T. H., JR. 1951. Origin of tetrapod limbs. Amer. Midl. Nat., 46: 245-251. JARVIK, E. 1952. On the fish-like tail in the ichthyostegid stegocephalians. Meddel. om Grønland, 114: 1-90. 1954. On the visceral skeleton in _Eusthenopteron_ with a discussion of the parasphenoid and palatoquadrate in fishes. Kgl. Svenska Vetenskapsakad. Handl., 5: 1-104. 1955. The oldest tetrapods and their forerunners. Sci. Monthly, 80: 141-154.