PAU, France -- The 100th Tour de France may go down as one of the greatest battles in the history of the race.

Lance Armstrong has suffered through crashes, near misses and dehydration in his pursuit of a record-tying fifth consecutive win. Instead of weakening, he is getting stronger with each passing day.

One would think riders would begin to wither during the third week of the Tour de France, due to the immense fatigue from the previous two weeks of racing. The amazing truth is that riders often get stronger as the race progresses.

The human body responds to stress by trying to adapt to it. It's one of the fundamental principles of training: you stress an athlete's physiological systems in order to force the body to adapt and get stronger.

It is nearly impossible to simulate the stress of a three-week stage race in training, but elite athletes are so well-conditioned that some of them can actually adapt during the race itself. Armstrong and Jan Ullrich are both riders who have historically gained strength as the Tour progressed. They adapt to the stress of the first part of the race and ride even better in the third week.

On top of gaining strength as he enters the final week of the Tour, Armstrong is also gaining confidence and momentum. His outstanding performance on Monday's Stage 15 summit finish to Luz-Ardiden gave him the stage win and time advantage he needed to confirm, to himself and everyone else, that he has the power to win his fifth consecutive Tour de France.

Talking to him during Tuesday's rest day, he told me, "Yesterday's win was not only important for gaining time but also for boosting my confidence that I will win my fifth Tour.''

With the Pyrenees behind them, the riders face several days of rolling hills and flat terrain before the final individual time trial on Saturday. The time gap between Armstrong and Ullrich is significant, but smaller than in any of Lance's previous victories. As a result, the U.S. Postal Service has to consider the possibility that the German may seek time bonuses available at intermediate sprints and stage finishes all the way to Paris. Winning an intermediate sprint provides six bonus seconds, and there are 20 bonus seconds awarded for winning a road stage.

Even if Ullrich or Armstrong decided to contest the intermediate sprints or stage finishes, they will have to fight the sprinters in the points competition. The points competition is very tight this year, with Fdjeux.com's Baden Cooke trying to win his first green jersey over defending points competition winner Robbie McEwen of the Lotto-Domo team. With these men and their teams working hard to secure points, it will be difficult, but not impossible, for either Armstrong or Ullrich to use the same sprints to gain valuable seconds.

Armstrong and Ullrich will keep a careful eye on each other throughout the remaining road stages of the Tour. They are both aware that Miguel Indurain, the only man to win five consecutive Tours, once attacked in the closing kilometers of a flat road stage and used his incredible time trial strength to hold off the rest of the charging peloton.

Armstrong remembers it well because he was right behind Indurain when he attacked, and despite his best efforts, couldn't keep up. Johan Bruyneel, now the U.S. Postal Service team director, was the only man who could stay with Indurain, and he ended up beating the Tour champion in the sprint for the stage victory.

More likely, the Tour de France will be decided in the final individual time trial Saturday. Despite losing the stage 12 time trial to Ullrich by a whopping 1:36, it is unlikely Ullrich will take the yellow jersey Saturday. Lance told me, "If I'm having a good day, I'm confident I can match or beat Jan in the time trial.''

Armstrong has precedent on his side for Saturday's time trial. He has won six of the eight long time trials in the Tour de France since his return from cancer in 1999. Prior to stage 12 this year, Armstrong had beaten Ullrich in Tour time trials by one minute or more.

Ullrich is definitely strong this year, but Lance lost the stage 12 time trial more due to dehydration than to lack of strength. He won't make the same mistake twice, and riding at full power he should be able to keep pace with the powerful German.

Chris Carmichael has been Lance Armstrong's coach since 1990 and has guided him to four consecutive Tour de France titles. He is writing a twice-weekly column for The Associated Press during the Tour de France.