Texas has Nebraska's Number

9 meetings as Big 12 Opponent
1st game 1996 Big 12 Championship
Texas' record against NU is 8-1
the one loss coming in the 1999 Big 12 Championship Game
5 Wins in a row against Nebraska.

Dec. 7, 1996 vs. #3 Nebraska W 37-27 Big12 CG
Oct. 31, 1998 @ #7 Nebraska W 20-16
Oct. 23, 1999 (#18) #3 Nebraska W 24-20
Dec. 4, 1999 (#12) vs. #3 Nebraska L 6-22 Big12 CG
Nov. 2, 2002 (#7) @ Nebraska W 27-24
Nov. 1, 2003(#16) #12 Nebraska W 31-7
Oct. 21, 2006 (#5) @ #17 Nebraska W 22-20
Oct. 27, 2007 (#19) Nebraska W 28-25
Dec. 5. 2009 (#3) vs. Nebraska * W 13-12 Big 12 CG

From http://www.mackbrown-texasfootball.com/sports/m-footbl/spec-rel/all-time-results.html