National organisations and individual organisers can surprise an unsuspecting foreign rider with additional requirements beyond the usual 'follow the route' and BRM regulations. Some of these additional requirements relate to the rider's equipment carried/ used during the ride.
I got caught out a few years ago because the UAF mandated helmets for all their brevets but didn't specifically advise so in the literature for each event (they do now). I ended up buying a helmet ten minutes before starting a 400 brevet celebrating Raymond Poulidor's birthday. Luckily for me, there was a bike shop at the start line and it was open.
Audax Oz requires riders to show the organiser two sets of front and rear lights and a reflective vest before starting any brevet where the maximum duration might extend into the hours of darkness. Cycle helmets are a legal requirement throughout Oz.
Randonneurs USA requires riders to wear reflective anklets at night, along with a reflective vest. "When riding all riders must wear an approved helmet."
I nearly wasn't able to do an Audax India Randonneurs brevet this year because "It is compulsory for the rider to display their rider number prominently on the front and rear of their bicycle, for the entire duration of the brevet. Riders not complying with this stipulation will not be permitted to start." The rider number is their AIR membership number. Scribbling on the back of a spare entry form, tearing it in half and using some zipties solved that problem.
http://www.audaxindia.org/rules-and-regulations.php Helmets are mandatory and tribars are banned.
BC Randonneurs require that a rider complete shorter brevets before attempting longer ones e.g. must have done a 200 sometime before attempting a 300. Cycle helmets are the law in parts of Canada; for all ages in British Columbia, New Brunswick and Nova Scotia and for under-18s in Alberta and Ontario but helmets are mandatory for Alberta Randonneurs, BC Randonneurs, Manitoba Randonneurs, Prairie Randonneurs, Randonneurs Nova Scotia and Randonneurs Ontario brevets. I expect that Club Velo Randonneurs de Montreal also requires helmets.
Helmets are the law in Israel (except in urban areas) but there are no penalties for not wearing a helmet. I've ridden Israeli brevets both with and without helmets.
There are other rules that I've not yet fallen foul of. Randonneurs Hong Kong mandates separate front and rear lights on the rider's helmet, in addition to front and rear lights on their bike.
https://sites.google.com/site/randonneurshk/mandatoryequipmentAre there other gotchas that might DQ a rider or prevent them from starting an overseas brevet?