The two Astana stars clearly have each other on their minds before the three-week race veers toward three tough days in the Pyrenees starting Friday, which may offer a glimpse as to which man is better suited to climbing the mountains that are crucial this year.
A day after a technical and crash-marred team time trial, they and other pre-race favorites were happy to cruise safely in the pack in Wednesday's 122-mile fifth stage.
Thomas Voeckler of France bared his brilliance in the breakaway by winning the wind-swept ride from the Mediterranean coastal town of Le Cap d'Agde, known for its nudist resort, to Perpignan.
Armstrong, who is but a split-second behind overall race leader Fabian Cancellara of Switzerland, and 2007 Tour champion Contador finished in the trailing peloton -- 7 seconds after the Frenchman.
The 37-year-old Texan has recounted his pre-stage tete-a-tetes with Contador each of the last two days -- suggesting that he sees his role as part mentor, part rival.
"I told Alberto that today was going to be complicated," the seven-time Tour champion said after Wednesday's stage, "so maybe he sees that I know what is going on in the Tour de France."
Officially the motto is teamwork, and they showed some by powering Astana to victory in the team time trial in Tuesday's Stage 4. But their words betray acknowledgment that a rivalry exists.
The buzz is about a two-man showdown with defending champion Carlos Sastre (2:44 back), two-time runner-up Cadel Evans (2:59 back) and Giro d'Italia winner Denis Menchov (3:52 behind). They are each strong climbers, and could still muster dazzling comebacks.
So far, Astana itself has the closest possible challengers to thwart any such duel. Contador is third overall, 19 seconds behind Armstrong. Former Tour runner-up Andreas Kloeden is fourth, 23 seconds back, and Levi Leipheimer is fifth, 31 seconds behind.
Cancellara isn't seen as a threat in the mountains.
The prospect that the Texan, who is in his comeback year after 3-1/2 years of retirement, could extend his record run of victories to eight is looking even more realistic. Armstrong has acknowledged he has had doubts earlier this season about whether he could do it.
Armstrong and the team "have started to believe he can win the Tour," his friend and fellow American Leipheimer said. "Of course we also believe that about Alberto, so we have a lot of parts to play."
Some evoke a possible replay of a bitter rivalry between French five-time Tour winner Bernard Hinault and teammate Greg Lemond in 1986, when the American won the first of his three titles.
"The two have nothing to do with each other," Contador said, referring to the comparison with him and Armstrong.
A tale of the tape could line up Armstrong's mental steeliness and proven ability to win against Contador's 26-year-old physique and ambition to prove that he can be one of cycling's greats.
Contador appears to like his chances at the next big race test, when riders start three days in the Pyrenees on Friday, with a Stage 7 ride from his native Spain to an uphill finish in Arcalis, Andorra.
"I can't wait to get to the mountains because it's my territory," Contador said. "The sensations are good, but I always like to confirm them."
The climax for the race this year comes in the next-to-last stage at the notorious Mont Ventoux, where Armstrong has never won in the Tour, a day before the July 26 finish in Paris.
Armstrong's leg power will be under scrutiny in the climbs.
"That's my question mark, that's your question mark, that's everybody's question mark," he said. "But we don't have to wait long until we'll find out, that's the good thing."
Armstrong seems perfectly aware that Contador will be physically stronger in the mountains -- but that that's not everything in bike racing.
"Strength does not come from physical capacity," Armstrong wrote on his Tweeter account, quoting Mahatma Gandhi. "It comes from an indomitable will."