Mark-recapture data on Phrynosoma cornutum from the Desert Biome Jornada Validation Sites since 1970 and our feeding behavior studies support the contention that these animals are not territorial. Individual lizards, followed for a day, have moved well over 100 meters and frequently approach within a meter of another P. cornutum. This type of encounter usually results in head bobbing and mutual retreat of the lizards. On 19 July 1972 the senior author observed physical combat between two male P. cornutum, hereafter designated A and B. The combat was not preceded by head bobbing display by either lizard and lasted for over an hour [(0851-1005 hours) mountain daylight time]... A detailed description of the combat follows.... To our knowledge this is the only report of combat in Phrynosoma although vigorous combat is common in inguanids.