I know in normal circumstances that a toss of a coin or a tee is used in most tournaments to determine who tees off first, but does anybody know how The Ryder Cup determines which team tees off first in the very first match. Is it a case of visitors go first?? Or do they use the same format- coin toss.

according to this page, it's by agreement:
www.rydercup.com/usa/about

Rules, Format & Terminology

Play is governed by the 2000 Rules of Golf as issued by The Royal & Ancient Golf Club of St. Andrews, and where applicable, by Local Rules.

Match Play, including foursomes (two-man teams in alternate shot), fourball (two-man teams in better ball) and singles (18 holes at match play). The order of play during the first two days of competition (foursomes or four-balls) is determined through mutual agreement of both teams' captains. There are a total of 28 matches.

Thanks, George! I see then there really is no set of rules of order other than probably a coin toss or something like it.

Just reread your response and noticed that it was for the order of play (fourball or foursomes) not for which team actually gets to tee off first. I think I need to search some more!!

hmm, I see! If the Ryder Cup Rules are silent on the point, they'd fall back to the rules of golf St. Andrew's Edition. Looks like it's determined by lot.

Rule 10 Order of Play
The side which shall have the honor at the first teeing ground shall be determined by the order of the draw. In the absence of a draw, the honor should be decided by lot.

Don't know if this is of any help but I found the following:

The Honor goes to the last player or team to win a hole. The player with the honor tees off first.

See: Honor

http://www.golfweb.com/tournaments/rydercup/2002/format/glossary.html

Thanks George, you're probably right about just by lot. Thanks for the info E.T. but that would come into play after the first hole unless there's something about the previous winner of the Ryder cup gets honours.