Audax is a style of long distance cycling event mostly popular in France, but also in Holland, Belgium and Germany. The term is now also commonly used to describe a different style of long distance cycling event found in many countries including France, Great Britain, Singapore, Australia, Canada and the USA.

The original form of the audax style involves riding in strict group formation at a steady pace set by a road captain. The group attempts to maintain a pace of 22.5 km/h between stops. The route is pre-planned with designated stopping points. For longer audax events the group may ride between 16 and 20 hours in a day before stopping at a designated sleeping location. The goal of the audax is to finish inside the prescribed time limit with all members of the group present. A support vehicle is allowed to follow each group of riders.[citation needed]

In some countries such as Australia and Great Britain, the term Audax is also used for randonnées. These are also long distance bicycle events, but riders are free to cycle at their own pace (French: allure libre), stop or sleep wherever they want and form groups randomly, provided they stay within the time limit.

The national organising bodies for allure libre riding in these counties (Audax Australia and Audax UK) both include the word ‘audax’ in their names. In addition, Audax Club Parisien now holds events such as the Paris–Brest–Paris (PBP) for the allure libre style, not the original audax style.[citation needed]. Brevet, or randonnée, is an organised long-distance bicycle ride in the sport of randonneuring. Cyclists – who, in this discipline, may be referred to as randonneurs – follow a designated but unmarked route (usually 200 km to 1400 km), passing through check-point controls, and must complete the course within specified time limits. These limits, while challenging, still allow the ride to be completed at a comfortable pace – there is no requirement to cycle at racing speeds or employ road bicycle racing strategies.

Randonnée is a French word which loosely translates to ‘ramble’ or ‘long journey’ (in French the verb ‘randonner’ originally means ‘hiking’, but is nowadays also used for bicycle and even motorized tours). Brevet means ‘certificate’ and refers to the card carried by randonneurs which gets stamped at controls; it is also used to refer to the event itself, ie: a certificated ride.

In Great Britain, Australia and Brazil the term audax is also used for brevets, although this term actually designates a different kind of long distance bicycling, see Audax. The French brevet club is called “Audax Club Parisien”, which increases the confusion.

Randonneurs do not compete against other cyclists; randonnées are a test of endurance, self-sufficiency and bicycle touring skills. Riders are expected to carry appropriate clothing for inclement weather, spare parts and tools needed for likely repairs. Brevets frequently involve night riding, when participants are required to carry lights, spare bulbs and reflective gear. No specialist bicycle is required; most riders use either a racing bicycle or a fast touring bicycle – several manufacturers provide models with a Randonneur or Audax name to reflect their target market. Those are usually racing bicycles with mounts for a baggage carrier and mudguards. On many brevets recumbents and velomobiles can be seen, as these types of bicycles are well suited for long distances.
From: http://en.wikipedia.org/wiki/Brevet_(cycling)