By Gene Cherry

EUGENE, Oregon (Reuters) - He wears the colors of the United States and she those of Canada, but Ashton Eaton and Brianne Theisen-Eaton will be on a joint mission at the Rio Olympics.

Never before has a married couple won gold medals at the same Olympics while representing different countries and they are determined to change that.

World indoor champions, they enter the Games with the best scores in the world this year - Eaton in the decathlon and Theisen-Eaton in the heptathlon.

"It would be the moonshot," Eaton, the 28-year-old world record holder and Olympic champion in the 10-event decathlon, said of a golden double.

For Theisen-Eaton, 27, the joy would be completing a nine-year journey.

"The gold medals together would be huge," the two-time world silver medallist told Reuters.

"But I think it is more like finishing that story, closing the book on that journey.

"Since 2007 when both of our careers kind of started and took off, we have trained together and we have been going through every day together.

"The two gold medals would be the cherry on top."

Small town North Americans - Eaton from Bend, Oregon, and Theisen-Eaton from Humboldt, Saskatchewan, their lives even have a Brazilian connection.

After meeting during Brianne's college recruiting trip to Oregon, they both competed in the 2007 Pan American Junior Championships in Sao Paulo, sparking a friendship that grew after Brianne joined Ashton at the University of Oregon.

They were married in 2013 and continue to live and train in Oregon.

Eaton's career has soared with five world records - three indoors and two outdoors - while Theisen-Eaton, 10th in the 2012 London Olympics, will be looking for her first major outdoor title.

Eaton should be ready "for a lot of points" at the Games, their long-time coach Harry Marra told Reuters, but there were no promises of a world record.

Sprints and hurdles, as always, will be Eaton's strengths.

So much so that even with hamstring and quadriceps problems, Eaton's winning score at the U.S trials, 8,750 points, was higher than the lifetime best of any Rio rival.

"It's a nice stat," said Marra, "but it will not make him overconfident.

"You never go into a multi-event (competition) over- confident. If you do, it will probably turn around and bite you somewhere."

For Theisen-Eaton, handling the pressure of top flight competition while owning the year's best score will be her biggest challenge.

In a similar scenario at last year's world championships in Beijing, "I let my mental side get the best of me," she said and she finished second behind British Olympic gold medallist and two-time world champion Jessica Ennis-Hill.

"Had I even scored a 100 points less than I did at Gotzis (where she set the year's top score), I still would have won."

Consistency has always been her trademark, Marra said.

"She is just steady all the way through," he said.

"If Brianne Theisen-Eaton is steady in Rio, I can guarantee you she's in the medals. Whether it is the gold, silver, bronze, I don't know."

(Editing by Greg Stutchbury)