Randonneuring: long-distance, unsupported endurance cycling. This style of riding is non-competitive in nature, and self-sufficiency is paramount. A Brevet or Brevet de Randonneur is an organised long-distance bicycle ride in the sport of randonneuring. Brevets are often colloquially called randonées or audax rides. (The term randonée is correct, but can also be applied to other types of distance cycling event. Audax is short-hand for Audax allure libre, and should not be confused with the original team-riding version of the Audax sport, which has distinct rules.)  (from Wikipedia)
These organizations sponsor or promote brevet rides.
LONE STAR Randonneurs
Promoting Long Distance Cycling in North Texas
Randonneuring in the Rio Grande Valley
Hill Country Randonneurs is an organization to promote randonneuring throughout central Texas.
Concho Valley Randonneurs
Promoting Long Distance Cycling Thru-Out the Concho Valley. We are headquartered in San Angelo, TX.