If the defining characteristic of a dynasty is three national championships over a span of uninterrupted dominance, then it's pretty easy to say which programs qualify and which do not. That is, until you read the details of the teams that didn't win three national championships. Florida State is not the only program that came within a game or two of being a dynasty.
Ohio State won national titles in 1954 (Associated Press) and 1957 (coaches). In 1961, the Football Writers Association selected the Buckeyes ahead of Alabama, which won the AP and coaches' polls. However, in the interim seasons, the Buckeyes barely won two-thirds of their games (29-13-3, .678) and even had a losing record in 1959 (3-5-1). Sorry, that's not a dynasty.
Texas won 30 consecutive games from 1968 to 1970. But the streak didn't begin until after the Longhorns began the 1968 season 0-1-1. They finished that season No. 3, won everything in 1969 and shared the national title with Nebraska in 1970. But Texas went 9-3 in 1971 and didn't finish No. 1 again until 2005.
[h=1]Just short of a dynasty[/h]
