text: what two teams in pro football since 1964 had never played until 2006?   none, the rotating schedule was put in place four years ago. we are repeating the afc vs nfc meaning they already played each other 4 years ago. the confrence divisions play each other every 3 years and started repeating last year. so all teams have played all the other teams. i think you mean which two teams have never played at the one's home, but that almost ruins the question because almost have to give the city. in that case if it was on sunday i'd guess st loius and kansas city.