Hollywood stars mix with Ryder Cup royalty in Scotland

(CNN) -- It is the one event in the golfing calendar where Hollywood stars add some gliltz and glamor to golf's premier European Tour pro-am event.

But this year, the great and good from America might be forgiven for keeping their distance from Europe's Ryder Cup royalty in Scotland.

Several of the pivotal members of the victorious European team are back to the day job after one of the greatest sporting comebacks of all time in Chicago.

Both actor Bill Murray and 18-time Olympic gold medal winning swimmer Michael Phelps were at Medinah Country Club, as the United States sunk to defeat from a seemingly unassailable position.

Read: Ryder Cup hero Lawrie: Hostile U.S. reception helped Europe

But though Martin Kaymer, who holed the crucial putt that meant the U.S could not win back the Ryder Cup, Paul Lawrie and Peter Hanson were playing, Phelps was still delighted to be involved.

Europe's historic Ryder Cup comeback

Greatest sporting drama of all time?

Golfers aim at Obama, Romney targets

LPGA winner reveals Olympic ambitions

"With all the history that is around you here, on these great courses, it is just an honour for me to play in this tournament," Phelps told the European Tour's official website.

"I was a bit nervous on the first tee, but it wasn't too bad. To be honest, it was more nerve-wracking watching the Ryder Cup last week!

"My partner Paul Casey was awesome to play with, and there were some good comments going back and forth between us during the round. He gave me some great tips and, by the end, was just telling me to hit it hard!"

As well as the trio of European players all four of Jose Maria Olazabal's vice captains were playing, including 2011 British Open Darren Clarke and Paul McGinley, who was playing with Paralympic 400m champion Oscar Pistorius.

The South African, known as 'Blade Runner', birdied the second hole at the notoriously difficult Carnoustie course and has two more rounds to come, at Kingsbarns and St Andrews' famous old course.

"It was very stressful for me this morning," said Pistorius. "It was a nervous time on that first tee, and I was just glad to get the ball past the ladies' tee! But then I got that net birdie and overall the day was an unbelievable experience for me.

"To play with Paul and to be in a four-ball with (2010 European Ryder Cup captain) Colin Montgomerie and (five-time Olympic gold medalist) Steve Redgrave was brilliant, especially as Steve and I have known each other a long time and we are good friends.

"But we didn't have a bet -- we kept it clean! There was a bit of a competitive spirit between us, so perhaps we'll have a little match later in the tournament."

Read: Did the U.S. throw away the Ryder Cup?

Of all the Ryder Cup contingent it was Kaymer who fared the best, the German shooting a two-under-par round at Carnoustie.

The 27-year-old has had a hectic week after his famous putt in Chicago, but said he was glad to be back out on the course.

"There have been plenty of congratulations," he said. "It's a very nice feeling to come to St Andrews and to come here to Carnoustie, and a lot of people were rooting for us on Sunday obviously and they were watching. It's very nice to hear.

"If you put everything in consideration: we won last week The Ryder Cup, this week I get to play with my manager and friend, Johann (Elliot), my brother is caddying for him, we're playing some of the best golf courses in the world, it's nice weather; so it's tough to beat."

Kaymer's solid round was nothing compared to tournament leader Branden Grace, who made an eagle and 10 birdies to break Lee Westwood's Kingsbarns course record with a round of 60.

The South African is on 12-under, two shots clear of Frenchman Victor Dubuisson, who broke the course record at St Andrews with a round of 62 -- topping Rory McIlroy's feat from the 2010 British Open.