The 1968 Texas Longhorns football team was an American football team that represented the University of Texas at Austin as a member of the Southwest Conference (SWC) during the 1968 NCAA University Division football season. In their 12th year under head coach Darrell Royal, the Longhorns compiled an overall record of 9âÂÂ1âÂÂ1, with a mark of 6âÂÂ1 in conference play, and finished as SWC co-champion. Texas concluded their season with a victory over Tennessee in the Cotton Bowl Classic.